Publications  of  Grigorii  Shishkin

      Number of papers:  230+
   Number of communications to scientific meetings:  100+
   Number of books:   4  


Books

  1. G.I. Shishkin. Grid Approximations of Singularly Perturbed Elliptic and Parabolic Equations. Russian Acad. Sci., Ural Branch, Ekaterinburg, 1992. 232 pp. (in Russian).

  2. J.J.H. Miller, E. O'Riordan, G.I. Shishkin. Fitted Numerical Methods for Singular Perturbation Problems. Error Estimates in the Maximum Norm for Linear Problems in One and Two Dimensions. World Scientific Publishing Co., Inc., Singapore, 1996. xiv + 166 pp. ISBN: 981-02-2462-1.

  3. P.A. Farrell, A.F. Hegarty, J.J.H. Miller, E. O'Riordan, G.I. Shishkin. Robust Computational Techniques for Boundary Layers. Applied Mathematics, 16. Chapman & Hall / CRC Press, Boca Raton, FL, 2000. xvi + 254 pp. ISBN: 1-58488-192-5.

  4. L.G. Vulkov, J.J.H. Miller, G.I. Shishkin (Eds.). Analytical and Numerical Methods for Convection-Dominated and Singularly Perturbed Problems. Nova Science Publishers, Inc., N.Y., 2000. 309 pp. ISBN: 1-56072-848-5.

Selected Papers

      1990      1991      1992      1993      1994      1995      1996      1997      1998     
      1999      2000      2001      2002      2003      2004     

  1. G.I. Shishkin. A certain heat problem with a free boundary. Dokl. Akad. Nauk SSSR, 1971, vol. 197, 1276-1279 (in Russian); transl. in Soviet Math. Dokl., 1971, vol. 12, 682-686.

  2. G.I. Shishkin. A certain problem of Stefan type with a discontinuous movable boundary. Dokl. Akad. Nauk SSSR, 1975, 224 (6), 1276-1278 (in Russian).

  3. G.I. Shishkin. The first boundary value problem for a second order equation with small parameters multiplying the derivatives. Differen. Uravnenija, 1977, 13 (2), 376-378 (in Russian).

  4. G.I. Shishkin. A difference scheme for the solution of an elliptic equation with a small parameter in a region with a curvilinear boundary. Zh. Vychisl. Mat. Mat. Fiz., 1978, 18 (6), 1466-1475 (in Russian).

  5. G.I. Shishkin. A difference scheme for the solution of elliptic equations with small parameters multiplying the derivatives. Mathematical models and numerical methods (Papers, Fifth Semester, Stefan Banach Internat. Math. Center, Warsaw, 1975), pp. 89-92 (in Russian). Banach Center Publ., 3, PWN, Warsaw, 1978.

  6. G.I. Shishkin. The numerical solution of elliptic equations with a small parameter multiplying the highest derivatives. Dokl. Akad. Nauk SSSR, 1979, 245 (4), 804-808 (in Russian); transl. in Soviet Math. Dokl., 1979, 20 (2), 368-371.

  7. G.I. Shishkin. The grid method for solving elliptic equations with discontinuous boundary conditions. Zh. Vychisl. Mat. i Mat. Fiz., 1979, 19 (3), 640-651 (in Russian).

  8. G.I. Shishkin. A difference scheme on a nonuniform grid for differential equations with a small parameter multiplying the highest-order derivative. Zh. Vychisl. Mat. Mat. Fiz., 1983, 23 (3), 609-619 (in Russian); transl. in USSR Comput. Math. Math. Phys., 1983, 23 (3), 59-66.

  9. G.I. Shishkin. Increasing the accuracy of solutions of difference schemes for parabolic equations with a small parameter multiplying the highest derivative. Zh. Vychisl. Mat. Mat. Fiz., 1984, 24 (6), 864-875 (in Russian).

  10. G.I. Shishkin. A difference scheme for a fourth-order differential equation with a small parameter multiplying the highest derivative. Dokl. Akad. Nauk SSSR, 1984, 275 (6), 1323-1326 (in Russian); transl. in Soviet Math. Dokl., 1984, 29 (2), 402-405.

  11. G.I. Shishkin. A difference scheme for a fourth-order ordinary differential equation with a small parameter multiplying the highest derivative. Differen. Uravneniya, 1985, 21 (10), 1734-1742 (in Russian); transl. in Differential Equations, 1985, 21 (10), 1169-1176.

  12. G.I. Shishkin. A difference scheme for a fourth-order elliptic equation with a small parameter multiplying the highest derivatives. Differen. Uravneniya, 1985, 21 (12), 2159-2165 (in Russian); transl. in Differential Equations, 1985, 21 (12), 1465-1470.

  13. G.I. Shishkin. Solution of a boundary value problem for an elliptic equation with small parameter multiplying the highest derivatives. Zh. Vychisl. Mat. i Mat. Fiz., 1986, 26 (7), 1019-1031 (in Russian).

  14. G.I. Shishkin. A difference scheme for an elliptic equation with a small parameter at the highest derivatives. Dokl. Akad. Nauk SSSR, 1986, 286 (1), 57-61 (in Russian); transl. in Soviet Math. Dokl., 1986, 33 (1), 49-53.

  15. G.I. Shishkin. Approximation of solutions of singularly perturbed boundary value problems with a corner boundary layer. Zh. Vychisl. Mat. i Mat. Fiz., 1987, 27 (9), 1360-1374 (in Russian).

  16. G.I. Shishkin. Approximation of the solutions of singularly perturbed boundary value problems with a corner boundary layer. Dokl. Akad. Nauk SSSR, 1987, 296 (1), 39-43 (in Russian); transl. in Soviet Math. Dokl., 1988, 36 (2), 240-244.

  17. G.I. Shishkin. A difference scheme for a singularly perturbed equation of parabolic type with a discontinuous initial condition. Dokl. Akad. Nauk SSSR, 1988, 300 (5), 1066-1070 (in Russian); transl. in Soviet Math. Dokl., 1988, 37 (3), 792-796.

  18. G.I. Shishkin. Grid approximation of singularly perturbed parabolic equations with internal layers. Sov. J. Numer. Anal. Math. Modelling, 1988, 3 (5), 392-407.

  19. G.I. Shishkin. A difference scheme for a singularly perturbed equation of parabolic type with a discontinuous boundary condition. Zh. Vychisl. Mat. i Mat. Fiz., 1988, 28 (11), 1649-1662 (in Russian); transl. in USSR Comput. Math. and Math. Phys., 1988, 28 (6), 32-41.

  20. G.I. Shishkin. Approximation of solutions of singularly perturbed boundary value problems for an elliptic differential equation with parabolic boundary layers. BAIL V (Shanghai, 1988), pp. 320-325, Boole Press Conf. Ser., 12, Boole, Dun Laoghaire, 1988.

  21. G.I. Shishkin. Approximation of solutions of singularly perturbed boundary value problems with a parabolic boundary layer. Zh. Vychisl. Mat. i Mat. Fiz., 1989, 29 (7), 963-977 (in Russian); transl. in USSR Comput. Maths. Math. Phys., 1989, 29 (4), 1-10.

  22. G.I. Shishkin. A difference scheme for a singularly perturbed equation of parabolic type with discontinuous coefficients and concentrated factors. Zh. Vychisl. Mat. i Mat. Fiz., 1989, 29 (9), 1277-1290 (in Russian); transl. in USSR Comput. Maths. Math. Phys., 1989, 29 (5), 9-19.

  23. G.I. Shishkin. Grid approximation of singularly perturbed elliptic equations with discontinuous boundary conditions. Sov. J. Numer. Anal. Math. Modelling, 1989, 4 (1), 69-85.

  24. G.I. Shishkin. Grid approximation of singularly perturbed boundary value problems with a regular boundary layer. Sov. J. Numer. Anal. Math. Modelling, 1989, 4 (5), 397-417.

    1990

  25. G.I. Shishkin. Grid approximation of singularly perturbed boundary value problems with convective terms. Sov. J. Numer. Anal. Math. Modelling, 1990, 5 (2), 173-187.

  26. G.I. Shishkin. Grid approximations of singularly perturbed elliptic equations in domains with characteristic faces. Soviet J. Numer. Anal. Math. Modelling, 1990, 5 (4-5), 327-343.

  27. G.I. Shishkin. Grid approximation of singularly perturbed elliptic equations in case of limit zero-order equations degenerating at the boundary. Sov. J. Numer. Anal. Math. Modelling, 1990, 5 (6), 523-548.

  28. G.I. Shishkin. Approximation of solutions of boundary value problems with a parabolic boundary layer. Numerical analysis and mathematical modelling, pp. 435-443 (in Russian). Banach Center Publ., 24, PWN, Warsaw, 1990.

    1991

  29. J. Miller, E. Mullarkey, E. O'Riordan, G. Shishkin. A simple recipe for uniformly convergent finite-difference schemes for singularly perturbed problems. C.R. Acad. Sci. Paris Ser. I Math., 1991, 312 (8), 643-648.

  30. J.J.H. Miller, G.I. Shishkin. On the construction of uniformly convergent finite difference schemes for singularly perturbed problems for quasilinear elliptic equations. In: Computational Methods for Boundary and Interior Layers in Several Dimensions, J.J.Miller ed., Boole Press, Dublin, 1991, 103-118.

  31. G.I. Shishkin. Difference approximation of a singularly perturbed quasilinear elliptic equation that degenerates into a first-order equation. Dokl. Akad. Nauk SSSR, 1991, 317 (4), 845-849 (in Russian); transl. in Soviet Math. Dokl., 1991, 43 (2), 562-566.

  32. G.I. Shishkin. Grid approximation of singularly perturbed boundary value problem for quasilinear elliptic equation degenerating into first-order equation. Sov. J. Numer. Anal. Math. Modelling, 1991, 6 (1), 61-81.

  33. G.I. Shishkin. Grid approximation of singularly perturbed boundary value problem for quasilinear parabolic equation in the case of complete degeneracy in spatial variables. Sov. J. Numer. Anal. Math. Modelling, 1991, 6 (3), 243-261.

  34. G.I. Shishkin. Grid approximation of certain singularly perturbed problems of convective transfer with diffusion. Sov. J. Numer. Anal. Math. Modelling, 1991, 6 (5), 395-420.

  35. G.I. Shishkin. Difference approximation of singularly perturbed parabolic equations that are degenerate on the boundary. Zh. Vychisl. Mat. i Mat. Fiz., 1991, 31 (10), 1498-1511 (in Russian).

  36. G.I. Shishkin. Grid approximation of a singularly perturbed boundary value problem for a quasilinear elliptic equation in the case of complete degeneration. Zh. Vychisl. Mat. i Mat. Fiz., 1991, 31 (12), 1808-1825 (in Russian).

    1992

  37. G.I. Shishkin. Difference approximation of a singularly perturbed boundary value problem for quasilinear elliptic equations degenerating into a first-order equation. Zh. Vychisl. Mat. i Mat. Fiz., 1992, 32 (4), 550-566 (in Russian); transl. in USSR Comput. Maths. Math. Phys., 1992, 32 (4), 467-480.

  38. G.I. Shishkin. A difference scheme for a singularly perturbed parabolic equation degenerating on the boundary. Zh. Vychisl. Mat. i Mat. Fiz., 1992, 32 (5), 717-732 (in Russian); transl. in USSR Comput. Maths. Math. Phys., 1992, 32 (5), 621-636.

  39. G.I. Shishkin. Grid approximation of singularly perturbed boundary-value problems with sharply changing density of sources. Rus. J. Numer. Anal. Math. Modelling, 1992, 7 (2), 145-167.

  40. G.I. Shishkin. Methods of constructing grid approximations for singularly perturbed boundary-value problems. Condensing-grid methods. Russ. J. Numer. Anal. Math. Modelling, 1992, 7 (6), 537-562.

    1993

  41. A.F. Hegarty, J.J.H. Miller, E. O'Riordan, G.I. Shishkin. Key to the computation of the transfer of a substance by convection-diffusion in a laminar fluid. In: Applications of Computational Methods for Boundary and Interior Layers, J.J.H. Miller ed., Boole Press, Dublin, 1993, 94-107.

  42. J.J.H. Miller, E. O'Riordan, E.A. Petrenko, G.I. Shishkin. Special finite difference methods for calculating heat fields in solid bodies with rapidly changing surface temperature. In: Applications of Computational Methods for Boundary and Interior Layers, J.J.H. Miller ed., Boole Press, Dublin, 1993, 108-123.

  43. G.I. Shishkin. Grid approximation of a singularly perturbed quasilinear equation in the presence of a transition layer. Dokl. Akad. Nauk, 1993, 328 (3), 299-302 (in Russian); transl. in Russian Acad. Sci. Dokl. Math., 1993, 47 (1), 83-88.

  44. G.I. Shishkin. Grid approximation of the Dirichlet problem for a singularly perturbed quasilinear parabolic equation in the presence of a transition layer. Dokl. Akad. Nauk, 1993, 332 (4), 424-427 (in Russian); transl. in Russian Acad. Sci. Dokl. Math., 1994, 48 (2), 346-352.

  45. G.I. Shishkin. Grid approximation of singularly perturbed degenerate elliptic equations. Zh. Vychisl. Mat. i Mat. Fiz., 1993, 33 (4), 541-560 (in Russian); transl. in Comput. Maths. Math. Phys., 1993, 33 (4), 493-509.

  46. G.I. Shishkin. Grid approximation of singularly perturbed quasilinear elliptic equations that degenerate into a zero-order equation. Zh. Vychisl. Mat. i Mat. Fiz., 1993, 33 (9), 1305-1323 (in Russian); transl. in Comp. Maths. Math. Phys., 1993, 33 (9), 1155-1170.

  47. G.I. Shishkin. Iterative grid methods for singularly perturbed elliptic equations degenerating into zero-order ones. Rus. J. Numer. Anal. Math. Modelling, 1993, 8 (4), 341-369.

  48. G.I. Shishkin. Method of splitting for singularly perturbed parabolic equations. East-West J. Numer. Math., 1993, 1 (2), 147-163.

  49. P.W. Hemker, G.I. Shishkin. Approximations of parabolic PDEs with a discontinuous initial condition. East-West J. Numer. Math., 1993, 1 (4), 287-302.

    1994

  50. A.F. Hegarty, J.J.H. Miller, E. O'Riordan, G.I. Shishkin. Special numerical methods for convection-dominated laminar flows at arbitrary Reynolds number. East-West J. Numer. Math., 1994, 2 (1), 65-74.

  51. A.F. Hegarty, J.J.H. Miller, E. O'Riordan, G.I. Shishkin. Use of central difference operators for the solution of singularly perturbed problems. Comms. in Numer. Methods in Engineering, 1994, 10 (4), 297-302.

  52. A.F. Hegarty, J.J.H. Miller, E. O'Riordan, G.I. Shishkin. On numerical experiments with central difference operators on special piecewise uniform meshes for problems with boundary layers. Notes on Numerical Fluid Mechanics, Vieweg-Verlag, 1994, vol. 46, 167-176.

  53. P.W. Hemker, G.I. Shishkin. Discrete approximation of singularly perturbed parabolic PDEs with a discontinuous initial condition. Comp. Fluid Dynamics J., 1994, 2 (4). 375-392.

  54. P.W. Hemker, G.I. Shishkin. On a class of singularly perturbed boundary value problems for which an adaptive mesh technique is necessary. In: Proceedings of the Second International Colloquium on Numerical Analysis, Plovdiv, Bulgaria, August 13-17, 1993, eds D.Bainov and V.Covachev. International Science Publishers, 1994, 83-92.

  55. G.I. Shishkin. Difference approximation of the method of additive separation of singularities for a singularly perturbed equation of parabolic type. Zh. Vychisl. Mat. i Mat. Fiz., 1994, 34 (5), 720-738 (in Russian); transl. in Comput. Maths. Math. Phys., 1994, 34 (5), 621-637.

  56. G.I. Shishkin. Grid approximation of singularly perturbed quasilinear elliptic and parabolic equations that degenerate into equations that do not contain spatial derivatives. Zh. Vychisl. Mat. i Mat. Fiz., 1994, 34 (11), 1632-1651 (in Russian); transl. in Comput. Maths. Math. Phys., 1994, 34 (11), 1403-1419.

  57. G.I. Shishkin. The method of additive separation of singularities for quasilinear singularly perturbed elliptic and parabolic equations. Zh. Vychisl. Mat. i Mat. Fiz., 1994, 34 (12), 1793-1814 (in Russian); transl. in Comput. Maths. Math. Phys., 1994, 34 (12), 1541-1558.

  58. G.I. Shishkin. Grid approximation of boundary value problem for singularly perturbed quasilinear elliptic equations in the case of limit equations that are degenerate on the boundary. Differen. Uravneniya, 1994, 30 (7), 1244-1258 (in Russian); transl. in Differential Equations, 1994, 30 (7), 1152-1166.

  59. G.I. Shishkin. Grid approximation of singularly perturbed equations degenerating on the boundary. The case of coefficients changing sharply in the neighborhood of a boundary layer. Mat. Model., 1994, 6 (5), 105-121 (in Russian).

    1995

  60. P.A. Farrell, A.F. Hegarty, J.J.H. Miller, E. O'Riordan, G.I. Shishkin. On the design of piecewise uniform meshes for solving advection-dominated transport equations to a prescribed accuracy. Notes on Numerical Fluid Mechanics, Vieweg-Verlag, 1995, 49, 86-95.

  61. A.F. Hegarty, J.J.H. Miller, E. O'Riordan, G.I. Shishkin. Numerical results for advection-dominated heat transfer in a moving fluid with a non-slip boundary condition. Intern. J. Numer. Meth. Heat & Fluid Flow, 1995, 5 (2), 131-140.

  62. A.F. Hegarty, J.J.H. Miller, E. O'Riordan, G.I. Shishkin. Special meshes for finite difference approximations to an advection-diffusion equation with parabolic layers. J. Comp. Phys., 1995, 117 (1), 47-54.

  63. A.F. Hegarty, J.J.H. Miller, E. O'Riordan, G.I. Shishkin. On a novel mesh for the regular boundary layers arising in advection-dominated transport in two dimensions. Comms. in Numer. Methods in Engineering, 1995, 11, 435-441.

  64. J.J.H. Miller, E. O'Riordan, G.I. Shishkin. On piecewise-uniform meshes for upwind and central difference operators for solving singularly perturbed problems. IMA J. Numer. Anal., 1995, 15 (1), 89-99.

  65. G.I. Shishkin. A difference scheme for the problem of the decay of a discontinuity in the case of the viscous Burgers equation. Dokl. Rus. Akad. Nauk, 1995, 342 (3), 313-317 (in Russian).

  66. G.I. Shishkin. Grid approximation of singularly perturbed boundary value problems for systems of elliptic and parabolic equations. Zh. Vychisl. Mat. i Mat. Fiz., 1995, 35 (4), 542-564 (in Russian); transl. in Comp. Maths. Math. Phys., 1995, 35 (4), 429-446.

  67. G.I. Shishkin. Grid approximation of boundary value problems for singularly perturbed quasilinear elliptic equations in the presence of a transitional layer. Mat. Model., 1995, 7 (2), 72-88 (in Russian).

  68. G.I. Shishkin. A problem for grid approximation of the diffusion flow in numerical modelling of pollution transport. Mat. Model., 1995, 7 (7), 61-80 (in Russian).

  69. G.I. Shishkin. Grid approximation of quasi-linear singularly perturbed elliptic and parabolic equations with mixed boundary conditions. Mat. Model., 1995, 7 (10), 111-126 (in Russian).

  70. P.N. Vabishchevich, G.I. Shishkin. Difference schemes on locally condensing grids. Differ. Uravn., 1995, 31 (7), 1179-1183 (in Russian); transl. in Differential Equations, 1995, 31 (7), 1121-1126.

  71. J.J.H. Miller, E. O'Riordan, G.I. Shishkin. On the use of fitted operator methods for singularly perturbed partial differential equations. In: Advanced Mathematics, Computations and Applications, Proceedings of the International Conference AMCA-95, Novosibirsk, June 20-24, 1995, eds. A.S.Alekseev and N.S.Bakvalov. NCC Publisher, Novosibirsk, 1995, 518-531.

  72. G.I. Shishkin. Grid approximation of the solution and diffusion flux for singularly perturbed parabolic equations. In: Proceedings of the 7-th International Conference on Boundary and Interior Layers: Computational and Asymptotic Methods, Beijing, China, 1994. International Academic Publishers, 1995, 12-19.

  73. I.V. Pershin, G.I. Shishkin, I.V. Tselishcheva. Parallelizing algorithms for the solution of boundary value problems for singularly perturbed elliptic equations. In: Algorithms and Programmed Tools of Parallel Computations. Ekaterinburg, Ural Branch of Rus. Acad. Sci., 1995, 125-147 (in Russian).

    1996

  74. P.A. Farrell, P.W. Hemker, G.I. Shishkin. Discrete approximations for singularly perturbed boundary value problems with parabolic layers, I. J. Comput. Maths., 1996, 14 (1), 71-97.

  75. P.A. Farrell, P.W. Hemker, G.I. Shishkin. Discrete approximations for singularly perturbed boundary value problems with parabolic layers, II. J. Comput. Maths., 1996, 14 (2), 183-194.

  76. P.A. Farrell, P.W. Hemker, G.I. Shishkin. Discrete approximations for singularly perturbed boundary value problems with parabolic layers, III. J. Comput. Maths., 1996, 14 (3), 273-290.

  77. P.A. Farrell, J.J.H. Miller, E. O'Riordan, G.I. Shishkin. A uniformly convergent finite difference scheme for a singularly perturbed semilinear equation. SIAM J. Numer. Anal., 1996, 33 (3), 1135-1149.

  78. G.I. Shishkin. Grid approximation of singularly perturbed equations with convective terms in the case of mixed boundary conditions. Differ. Uravn., 1996, 32 (5), 689-701 (in Russian); transl. in Differential Equations, 1996, 32 (5), 698-711.

  79. G.I. Shishkin. Locally one-dimensional difference schemes for singularly perturbed parabolic equations. Zh. Vychisl. Mat. i Mat. Fiz., 1996, 36 (2), 42-61 (in Russian); transl. in Comp. Maths. Math. Phys., 1996, 36 (2), 165-180.

  80. G.I. Shishkin. Grid approximation of parabolic equations with singular initial conditions. Zh. Vychisl. Mat. i Mat. Fiz., 1996, 36 (3), 73-92 (in Russian); transl. in Comp. Maths. Math. Phys., 1996, 36 (3), 341-356.

  81. G.I. Shishkin. Approximation of solutions and diffusion flows in the case of singularly perturbed boundary value problems with discontinuous initial conditions. Zh. Vychisl. Mat. i Mat. Fiz., 1996, 36 (9), 83-104 (in Russian); transl. in Comp. Maths. Math. Phys., 1996, 36 (9), 1233-1250.

  82. G.I. Shishkin. The method of improving the accuracy of the approximate solutions to singularly perturbed equations by defect correction. Rus. J. Numer. Anal. Math. Model., 1996, 11 (6), 539-557.

  83. G.I. Shishkin. Grid approximation of singularly perturbed quasi-linear elliptic equations in the case of multiple solutions of the reduced equation. Mat. Model., 1996, 8 (7), 109-127 (in Russian).

  84. G.I. Shishkin, I.V. Tselishcheva. Parallel methods of solving singularly perturbed boundary value problems for elliptic equations. Mat. Model., 1996, 8 (3), 111-127 (in Russian, English summary).

  85. G.I. Shishkin, P.N. Vabishchevich. Parallel domain decomposition methods with the overlapping of subdomains for parabolic problems. Math. Models and Methods in Applied Sciences, 1996, 6 (8), 1169-1185.

    1997

  86. A.F. Hegarty, J.J.H. Miller, E. O'Riordan, G.I. Shishkin. Numerical solution of elliptic convection-diffusion problems on fitted meshes. CWI Quarterly, 1997, 10 (3&4), 239-251.

  87. P.W. Hemker, G.I. Shishkin, L.P. Shishkina. The use of defect correction for the solution of parabolic singular perturbation problems, ZAMM - Z. angew. Math. Mech., 1997, 77 (1), 59-74.

  88. V.L. Kolmogorov, G.I. Shishkin. Numerical methods for singularly perturbed boundary value problems modelling diffusion processes. In: Singular Perturbation Problems in Chemical Physics (J.J.H. Miller ed.), Advances in Chemical Physics Series, vol. XCVII, J.Wiley & Sons, 1997, 181-362.

  89. G.I. Shishkin. Grid approximation of a singularly perturbed Neumann problem for parabolic equations in the case of a discontinuous boundary function. Zh. Vychisl. Mat. Mat. Fiz., 1997, 37 (3), 378-381 (in Russian); transl. in Comp. Math. Math. Phys., 1997, 37 (3), 370-373.

  90. G.I. Shishkin. Singularly perturbed boundary value problems with concentrated sources and discontinuous initial conditions. Zh. Vychisl. Mat. Mat. Fiz., 1997, 37 (4), 429-446 (in Russian); transl. in Comp. Math. Math. Phys., 1997, 37 (4), 417-434.

  91. G.I. Shishkin. On finite difference fitted schemes for singularly perturbed boundary value problems with a parabolic boundary layer. J. Math. Anal. & Applications, 1997, 208, 181-204.

  92. G.I. Shishkin. Acceleration of the process of the numerical solution to singularly perturbed boundary value problems for parabolic equations on the basis of parallel computations. Rus. J. Numer. Anal. Math. Model., 1997, 12 (3), 271-291.

  93. G.I. Shishkin, L.P. Shishkina, P.W. Hemker. A numerical method with floating meshes for singularly perturbed problems with a concentrated disturbance of the initial data. CWI Qurterly, 1997, 10 (3&4), 317-336.

  94. G.I. Shishkin, I.V. Tselishcheva. The decomposition method for singularly perturbed boundary value problems with local perturbation of initial conditions. Equations with convective terms. Izv. Vyssh. Uchebn. Zaved. Mat., 1997, No. 4, 98-107 (in Russian); transl. in Russian Math. (Izv. VUZ), 1997, 41 (4), 96-105.

  95. C. Clavero, J.C. Jorge, F. Lisbona, G.I. Shishkin. Splitting time method and one dimensional special meshes for reaction-diffusiion parabolic problems. In: Numerical Analysis and Its Applications, First Intern. Workshop, WNAA'96, Rousse, Bulgaria, June 1996. Proceedings (L.Vulkov, J.Wasniewski and P.Yalamov eds.) / Lecture Notes in Computer Science, Springer-Verlag, 1997, vol. 1196, 106-113.

  96. V.L. Kolmogorov, G.I. Shishkin and L.P. Shishkina. Numerical analysis in singularly perturbed boundary value problems modelling heat transfer processes. In: Numerical Analysis and Its Applications, First Intern. Workshop, WNAA'96, Rousse, Bulgaria, June 1996. Proceedings (L.Vulkov, J.Wasniewski and P.Yalamov eds.) / Lecture Notes in Computer Science, Springer-Verlag, 1997, vol. 1196, 250-257.

  97. J.J.H. Miller, E. O'Riordan, G.I. Shishkin. Fitted mesh methods for the singularly perturbed reaction diffusion problem. In: Proceedings of the V-th International Colloquium on Numerical Analysis, Plovdiv, Bulgaria, August 13-17, 1996, ed. E.Minchev. Academic Publications, 1997, 99-105.

  98. G.I. Shishkin. Grid approximations of the solution and diffusion flux for singularly perturbed equations with Neumann boundary conditions. In: Numerical Analysis and Its Applications, First Intern. Workshop, WNAA'96, Rousse, Bulgaria, June 1996. Proceedings, (L.Vulkov, J.Wasniewski and P.Yalamov eds.) / Lecture Notes in Computer Science, Springer-Verlag, 1997, vol. 1196, 430-441.

  99. G.I. Shishkin. Grid approximations for singularly perturbed parabolic equations with discontinuous coefficients and concentrated factors. Proc. of 9th Intern. Conference "Computational Modeling and Computing in Physics" (Dubna, 1996). Joint Inst. Nuclear Res., Dubna, 1997, 253-258.

    1998

  100. C. Clavero, J.J.H. Miller, E.O'Riordan, G.I. Shishkin. An accurate numerical solution of a two dimensional heat transfer problem with a parabolic boundary layer. J. Comp. Math., 1998, 16 (1), 27-39.

  101. C. Clavero, J.C. Jorge, F.Lisbona, G.I. Shishkin. A fractional step method on a special mesh for the resolution of multidimensional evolutionary convection-diffusion problems. Appl. Numer. Math., 1998, 27 (3), 211-232.

  102. P.A. Farrell, J.J.H. Miller, E. O'Riordan, G.I. Shishkin. On the non-existence of e-uniform finite difference methods on uniform meshes for semilinear two-point boundary value problems. Math. Comp., 1998, 67 (222), 603-617.

  103. J.J.H. Miller, E. O'Riordan, G.I. Shishkin, L.P. Shishkina. Fitted mesh methods for problems with parabolic boundary layers. Mathematical Proceedings of the Royal Irish Academy, 1998, 98A (2), 173-190.

  104. G.I. Shishkin. Grid approximations of singularly perturbed systems of parabolic convection-diffusion equations with counterflow. Siberian J. Numer. Math., 1998, 1 (3), 281-297.

  105. G.I. Shishkin. A grid approximation for the Riemann problem in the case of the Burgers equation. Zh. Vychisl. Mat. Mat. Fiz., 1998, 38 (8), 1418-1420 (in Russian); transl. in Comp. Math. Math. Phys., 1998, 38 (8), 1361-1363.

  106. G.I. Shishkin. Approximation of singularly perturbed elliptic equations with convective terms in the case of a flow impinging on an impermeable wall. Zh. Vychisl. Mat. Mat. Fiz., 1998, 38 (11), 1844-1859 (in Russian); transl. in Comp. Math. Math. Phys., 1998, 38 (11), 1768-1782.

  107. G.I. Shishkin. Finite-difference approximations of singularly perturbed elliptic equations. Zh. Vychisl. Mat. Mat. Fiz., 1998, 38 (12), 1989-2001 (in Russian); transl. in Comp. Math. Math. Phys., 1998, 38 (12), 1909-1921.

  108. G.I. Shishkin. Grid approximation of singularly perturbed systems of elliptic and parabolic equations with convective terms. Differen. Uravneniya, 1998, 34 (12), 1686-1696 (in Russian); transl. in Differential Equations, 1998, 34 (12), 1693-1704.

  109. G.I. Shishkin. A posteriori piecewise uniform grids for singularly perturbed elliptic equations of a reaction-diffusion type. Rus. J. Numer. Anal. Math. Modelling, 1998, 13 (5), 411-423.

  110. G.I. Shishkin. Grid approximations of parabolic equations with a small parameter multiplying the space and time derivatives. Reaction-diffusion equations. Mathematica Balkanica. New Series, 1998, 12 (1&2), 179-214.

  111. P.A. Farrell, G.I. Shishkin. On the convergence of iterative methods for linear systems arising from singularly perturbed equations. Proc. of Copper Mountain Conf. on Iterative Methods, 1998, 1-7.

  112. P.W. Hemker, G.I. Shishkin, L.P. Shishkina. A defect correction method for parabolic singular perturbation problems on a rectangle. Proceedings of the Second International Conference "Finite-Difference Methods: Theory and Application", Minsk, 1998. V. 2. P. 30-34.

  113. J.J.H. Miller, E. O'Riordan and G.I. Shishkin. Fitted numerical methods for four simple convection-diffusion problems. Proceedings of the Second Asian Mathematical Conference on Numerical Analysis, Thailand 1995 (Nakhon Ratchasima), S. Tangmanee and E. Schulz eds., World Sci. Publishing, River Edge, NJ, 1998. P. 444-448.

  114. G.I. Shishkin. A decomposition method for singularly perturbed reaction-diffusion equations with discontinuous boundary conditions. Proceedings of the Second International Conference "Finite-Difference Methods: Theory and Application", Minsk, 1998. V. 3. P. 77-84.

    1999

  115. G.I. Shishkin. Singularly perturbed boundary value problems with locally perturbed initial conditions. Equations with convective terms. Zh. Vychisl. Mat. Mat. Fiz., 1999, 39 (2), 262-279 (in Russian); transl. in Comp. Math. Math. Phys., 1999, 39 (2), 249-265.

  116. G.I. Shishkin. Increasing the accuracy of approximate solutions by residual correction for singularly perturbed equations with convective terms. Izv. Vyssh. Uchebn. Zaved. Mat., 1999, No. 5, 81-93 (in Russian); transl. in Russian Math. (Iz. VUZ), 1999, 43 (5), 77-89.

  117. G.I. Shishkin. Optimization of piecewise-uniform grids for singularly perturbed equations of reaction-diffusion type. Differen. Uravneniya, 1999, 35 (7), 990-997 (in Russian); transl. in Differential Equations, 1999, 35 (7), 1000-1007.

  118. G.I. Shishkin. Grid approximation of singularly perturbed boundary value problems in a nonconvex domain with a piecewise smooth boundary. Mat. Model., 1999, 11 (11), 75-90 (in Russian).

  119. G.I. Shishkin. Grid approximation of singularly perturbed boundary value problems on locally refined meshes. Reaction-diffusion equations. Mat. Model., 1999, 11 (12), 87-104 (in Russian).

  120. G.I. Shishkin. Locally one-dimensional difference schemes for singularly perturbed parabolic equations with convective terms. Rus. J. Numer. Anal. Math. Modelling, 1999, 14 (6), 495-511.

  121. P.A. Farrell, A. Hegarty, J.J.H. Miller, E. O'Riordan, G.I. Shishkin. On a fitted operator technique for singular perturbation equations. In: Finite Difference Methods: Theory and Applications (A.A. Samarskii, L.G. Vulkov and P.N. Vabishchevich eds.), [Proceedings of the International Conference, Rousse, Bulgaria, August 10-13, 1997], Nova Science, N.Y., 1999, 71-78.

  122. P.W. Hemker, G.I. Shishkin, L.P. Shishkina. The numerical solution of a Neumann problem for parabolic singular perturbed equations with high-order time accuracy. In: Recent Advances in Numerical Methods and Applications II (O.P. Iliev, M.S. Kaschiev, S.D. Margenov, B.H. Sendov and P.S. Vassilevski eds.), Proceedings of the Fourth International Conference, Sofia, Bulgaria, August 19-23, 1998, World Scientific, Singapore, 1999, 27-39.

  123. P.W. Hemker, G.I. Shishkin, L.P. Shishkina. An e-uniform defect-correction method for a parabolic convection-diffusion problem. In: Recent Advances in Numerical Methods and Applications II (O.P. Iliev, M.S. Kaschiev, S.D. Margenov, B.H. Sendov and P.S. Vassilevski eds.), Proceedings of the Fourth International Conference, Sofia, Bulgaria, August 19-23, 1998, World Scientific, Singapore, 1999, 521-529.

  124. G.I. Shishkin. Grid approximation of singularly perturbed parabolic equations with convective terms in the case of impermeable walls. In: Finite Difference Methods: Theory and Applications (A.A. Samarskii, L.G. Vulkov and P.N. Vabishchevich eds.), [Proceedings of the International Conference, Rousse, Bulgaria, August 10-13, 1997], Nova Science, N.Y., 1999, 229-239.

  125. G.I. Shishkin. Grid approximation of singularly perturbed elliptic equations with convective terms in unbounded domains. In: Recent Advances in Numerical Methods and Applications II (O.P. Iliev, M.S. Kaschiev, S.D. Margenov, B.H. Sendov and P.S. Vassilevski eds.), Proceedings of the Fourth International Conference, Sofia, Bulgaria, August 19-23, 1998, World Scientific, Singapore, 1999, 547-555.

  126. G.I. Shishkin, I.V. Tselishcheva. Approximations of the solution and diffusion fluxes for singularly perturbed parabolic equations with convective terms on a rectangle. In: Finite Difference Methods: Theory and Applications (A.A. Samarskii, L.G. Vulkov and P.N. Vabishchevich eds.), [Proceedings of the International Conference, Rousse, Bulgaria, August 10-13, 1997], Nova Science, N.Y., 1999, 241-249.

  127. I.V. Tselishcheva, G.I. Shishkin. A decomposition method for singularly perturbed reaction-diffusion equations. In: Recent Advances in Numerical Methods and Applications II (O.P. Iliev, M.S. Kaschiev, S.D. Margenov, B.H. Sendov and P.S. Vassilevski eds.), Proceedings of the Fourth International Conference, Sofia, Bulgaria, August 19-23, 1998, World Scientific, Singapore, 1999, 556-564.

    2000

  128. C. Clavero, J.C. Jorge, F.Lisbona, G.I. Shishkin. An alternating direction scheme on a nonuniform mesh for reaction-diffusion parabolic problems. IMA J. Numer. Anal., 2000, 20 (2), 263-280.

  129. P.W. Hemker, G.I. Shishkin, L.P. Shishkina. e-uniform schemes with high-order time-accuracy for parabolic singular perturbation problems. IMA J. Numer. Anal., 2000, 20 (1), 99-121.

  130. P.W. Hemker, G.I. Shishkin, L.P. Shishkina. Distributing the numerical solution of parabolic singularly perturbed problems with defect correction over independent processes. Siberian J. Numer. Mathematics, 2000, 3 (3), 229-258.

  131. J.J.H. Miller, E. O'Riordan, G.I. Shishkin, S. Wang. A parameter-uniform Schwarz method for a singularly perturbed reaction-diffusion problem with an interior layer. Applied Numerical Mathematics, 2000, 35 (4), 323-337.

  132. G.I. Shishkin. Grid approximation of the transport equation for the Prandtl problem of flow past a plate at high Reynolds numbers. Dokl. Rus. Akad. Nauk, 2000, 374 (1), 23-25 (in Russian); English transl. in Doklady Mathematics, 2000, 62 (2), 166-186.

  133. G.I. Shishkin. Grid approximation of singularly perturbed boundary value problems on locally condensing grids. Convection-diffusion equations. Zh. Vychisl. Mat. Mat. Fiz., 2000, 40 (5), 714-725 (in Russian); transl. in Comp. Math. Math. Phys., 2000, 40 (5), 680-691.

  134. G.I. Shishkin. Approximation of systems of convection-diffusion elliptic equations with parabolic boundary layers. Zh. Vychisl. Mat. Mat. Fiz., 2000, 40 (11), 1648-1662 (in Russian); transl. in Comp. Math. Math. Phys., 2000, 40 (11), 1582-1595.

  135. G.I. Shishkin, P.N. Vabishchevich. Interpolation finite difference schemes on grids locally refined in time. Computer Methods in Applied Mechanics and Engineering, 2000, vol. 190, no. 8-10, 889-901.

  136. P.A. Farrell, J.J.H. Miller, E. O'Riordan, G.I. Shishkin. Singularly perturbed differential equations with discontinuous source terms. In: Analytical and Numerical Methods for Convection-Dominated and Singularly Perturbed Problems (L.G. Vulkov, J.J.H. Miller and G.I. Shishkin eds.), [Proceedings of the International Workshop, Lozenetz, Bulgaria, August 27-31, 1998], Nova Science, N.Y., 2000, 23-32.

  137. P.A. Farrell, G.I. Shishkin. Schwartz methods for singularly perturbed convection-diffusion problems. In: Analytical and Numerical Methods for Convection-Dominated and Singularly Perturbed Problems (L.G. Vulkov, J.J.H. Miller and G.I. Shishkin eds.), [Proceedings of the International Workshop, Lozenetz, Bulgaria, August 27-31, 1998], Nova Science, N.Y., 2000, 33-42.

  138. P.W. Hemker, G.I. Shishkin, L.P. Shishkina. Parallel methods based on a defect correction technique for parabolic singularly perturbed problems. In: Analytical and Numerical Methods for Convection-Dominated and Singularly Perturbed Problems (L.G. Vulkov, J.J.H. Miller and G.I. Shishkin eds.), [Proceedings of the International Workshop, Lozenetz, Bulgaria, August 27-31, 1998], Nova Science, N.Y., 2000, 43-50.

  139. S. Matthews, J.J.H. Miller, E. O'Riordan, G.I. Shishkin. A parameter robust numerical method for a system of singularly perturbed ordinary differential equations. In: Analytical and Numerical Methods for Convection-Dominated and Singularly Perturbed Problems (L.G. Vulkov, J.J.H. Miller and G.I. Shishkin eds.), [Proceedings of the International Workshop, Lozenetz, Bulgaria, August 27-31, 1998], Nova Science, N.Y., 2000, 219-224.

  140. H. MacMullen, J.J.H. Miller, E. O'Riordan, G.I. Shishkin. Schwarz iterative method for convection-diffusion problems with boundary layers. In: Analytical and Numerical Methods for Convection-Dominated and Singularly Perturbed Problems (L.G. Vulkov, J.J.H. Miller and G.I. Shishkin eds.), [Proceedings of the International Workshop, Lozenetz, Bulgaria, August 27-31, 1998], Nova Science, N.Y., 2000, 213-218.

  141. G.I. Shishkin. Approximation of singularly perturbed convection-diffusion equations with low smoothness of the derivatives involved in the equation. In: Analytical and Numerical Methods for Convection-Dominated and Singularly Perturbed Problems (L.G. Vulkov, J.J.H. Miller and G.I. Shishkin eds.), [Proceedings of the International Workshop, Lozenetz, Bulgaria, August 27-31, 1998], Nova Science, N.Y., 2000, 111-121.

  142. I.V. Tselishcheva, G.I. Shishkin. A decomposition method for quasilinear singularly perturbed parabolic equations in the reaction-diffusion case. In: Analytical and Numerical Methods for Convection-Dominated and Singularly Perturbed Problems (L.G. Vulkov, J.J.H. Miller and G.I. Shishkin eds.), [Proceedings of the International Workshop, Lozenetz, Bulgaria, August 27-31, 1998], Nova Science, N.Y., 2000, 251-257.

  143. B. Gahan, J.J.H. Miller, G.I. Shishkin. Accurate numerical method for Blasius' problem for flow past a flat plate with mass transfer. In: Finite Difference Schemes: Theory and Applications (R. Ciegis, A. Samarskii and M. Sapagovas eds.), Proc. of the 3rd International Conference FDS2000, Palanga, Lithuania. September 1-4, 2000. IMI, Vilnius, 2000, 63-74.

  144. G.I. Shishkin. On numerical methods on adaptive meshes for a singularly perturbed reaction-diffusion equation with a moving concentrated source. In: Finite Difference Schemes: Theory and Applications (R. Ciegis, A. Samarskii and M. Sapagovas eds.), Proc. of the 3rd International Conference FDS2000, Palanga, Lithuania. September 1-4, 2000. IMI, Vilnius, 2000, 205-214.

  145. G.I. Shishkin, P.A. Farrell, A.F. Hegarty, J.J.H. Miller, E. O'Riordan. On Reynolds-uniform numerical methods, in parabolic boundary layer regions, for Prandtl's problems. In: Finite Difference Schemes: Theory and Applications (R. Ciegis, A. Samarskii and M. Sapagovas eds.), Proc. of the 3rd International Conference FDS2000, Palanga, Lithuania. September 1-4, 2000. IMI, Vilnius, 2000, 215-225.

    2001

  146. C. Clavero, J.J.H. Miller, E. O'Riordan, G.I. Shishkin. Numerical experiments for advection-diffusion problems in a channel with a 180 deg. bend. Applied Mathematics and Computation, 2001, 118 (2-3), 223-246.

  147. P.A. Farrell, E. O'Riordan, J.J.H. Miller, G.I. Shishkin. Parameter-uniform fitted mesh method for quasilinear differential equations with boundary layers. Computational Methods in Applied Mathematics, 2001, 1 (2), 154-172.

  148. P.W. Hemker, G.I. Shishkin, L.P. Shishkina. High-order time-accurate parallel schemes for parabolic singularly perturbed problems with convection. Computing, 2001, 66 (2), 139-161.

  149. H. MacMullen, J.J.H. Miller, E. O'Riordan, G.I.Shishkin. A second order parameter-uniform overlapping Schwartz method for reaction-diffusion problems with boundary layers. Journal of Computational and Applied Mathematics, 2001, 130 (1-2), 231-244.

  150. A.A. Samarskii, V.I. Mazhukin, P.P. Matus, G.I. Shishkin. Monotone difference schemes for equations with mixed derivatives. Mat. Model., 2001, 13 (2), 17-26 (in Russian).

  151. G.I. Shishkin. On finite difference schemes for singularly perturbed problems with an initial parabolic layer. Communications in Applied Analysis, 2001, 5 (1), 1-16.

  152. G.I. Shishkin. Approximation of singularly perturbed parabolic reaction-diffusion equations with nonsmooth data. Computational Methods in Applied Mathematics, 2001, 1 (3), 298-315.

  153. G.I. Shishkin. Discrete approximation of the Riemann problem for the viscous Burgers equation. Mathematical Proceedings of the Royal Irish Academy, 2001, 101A (1), 27-48.

  154. G.I. Shishkin. Optimal piecewise uniform grids for singularly perturbed equations of a convection-diffusion type. Rus. J. Numer. Anal. Math. Modelling, 2001, 16 (2), 157-174.

  155. G.I. Shishkin. Grid approximation of the solution to the Blasius equation and of its derivatives. Zh. Vychisl. Mat. Mat. Fiz., 2001, 41 (1), 39-56 (in Russian); transl. in Comput. Maths. Math. Phys., 2001, 41 (1), 37-54.

  156. G.I. Shishkin. Grid approximation of singularly perturbed equations with convective terms under perturbation of data. Zh. Vychisl. Mat. Mat. Fiz., 2001, 41 (5), 692-707 (in Russian); transl. in Comput. Maths. Math. Phys., 2001, 41 (5), 649-664.

  157. G.I. Shishkin. The decomposition method for singularly perturbed parabolic convection-diffusion equations with discontinuous initial conditions. Siberian J. Numer. Mathematics, 2001, 4 (1), 85-106 (in Russian).

  158. G.I. Shishkin. Grid approximation of a wave equation singularly perturbed with respect to the space variable. Izv. Vyssh. Uchebn. Zaved. Mat., 2001, No. 1, 67-81 (in Russian).

  159. G.I. Shishkin. A posteriori adapted (to the solution gradient) grids in the approximation of singularly perturbed convection-diffusion equations. Vychisl. Tekhnol. (Computational Technologies), 2001, 6 (1), 72-87 (in Russian).

  160. G.I. Shishkin. Approximation of singularly perturbed reaction-diffusion equations on adaptive meshes. Mat. Model., 2001, 13 (3), 103-118 (in Russian).

  161. G.I. Shishkin. The method of total approximation for singularly perturbed elliptic equations with convective terms. Mat. Model., 2001, 13 (4), 95-108 (in Russian).

  162. G.I. Shishkin. A grid approximation to the transport equation in the problem on a flow past a flat plate at large Reynolds numbers. Differen. Uravneniya, 2001, 37 (3), 415-424 (in Russian); transl. in Differential Equations, 2001, 37 (3), 444-453.

  163. G.I. Shishkin. Grid apporximations of singularly perturbed parabolic equations with turning points. Differen. Uravneniya, 2001, 37 (7), 987-999 (in Russian); transl. in Differential Equations, 2001, 37 (7), 1037-1050.

  164. A.R. Ansari, A.F. Hegarty, G.I. Shishkin. A parameter robust numerical method for a problem with a symmetry boundary layer. In: Numerical Analysis and Its Applications: Second International Conference, NAA 2000, Rousse, Bulgaria, June 2000; Revised Papers, L.Vulkov, J.Wasniewski and P.Yalamov (Eds.) / Lecture Notes in Computer Science; Vol. 1988. Springer, 2001. P. 18-26.

  165. R.K. Dunne, E. O'Riordan, G.I. Shishkin. Singularly perturbed parabolic problems on non-rectangular domains. In: Numerical Analysis and Its Applications: Second International Conference, NAA 2000, Rousse, Bulgaria, June 2000; Revised Papers, L.Vulkov, J.Wasniewski and P.Yalamov (Eds.) / Lecture Notes in Computer Science; Vol. 1988. Springer, 2001. P. 265-272.

  166. P.A. Farrell, A.F. Hegarty, J.J.H. Miller, E. O'Riordan, G.I. Shishkin. Parameter-uniform numerical methods for a class of singularly perturbed problems with a Neumann boundary conditions. In: Numerical Analysis and Its Applications: Second International Conference, NAA 2000, Rousse, Bulgaria, June 2000; Revised Papers, L.Vulkov, J.Wasniewski and P.Yalamov (Eds.) / Lecture Notes in Computer Science; Vol. 1988. Springer, 2001. P. 292-303.

  167. B. Gahan, J.J.H. Miller, G.I. Shishkin. Reynolds-uniform numerical method for Prandtl's problem with suction-blowing based on Blasius' approach. In: Numerical Analysis and Its Applications: Second International Conference, NAA 2000, Rousse, Bulgaria, June 2000; Revised Papers, L.Vulkov, J.Wasniewski and P.Yalamov (Eds.) / Lecture Notes in Computer Science; Vol. 1988. Springer, 2001. P. 304-315.

  168. P.W. Hemker, G.I. Shishkin, L.P. Shishkina. Acceleration by parallel computations of solving high-order time-accurate difference schemes for singularly perturbed convection-diffusion problems. In: Numerical Analysis and Its Applications: Second International Conference, NAA 2000, Rousse, Bulgaria, June 2000; Revised Papers, L.Vulkov, J.Wasniewski and P.Yalamov (Eds.) / Lecture Notes in Computer Science; Vol. 1988. Springer, 2001. P. 393-401.

  169. H. MacMullen, E. O'Riordan, G.I. Shishkin. Schwarz methods for convection-diffusion problems. In: Numerical Analysis and Its Applications: Second International Conference, NAA 2000, Rousse, Bulgaria, June 2000; Revised Papers, L.Vulkov, J.Wasniewski and P.Yalamov (Eds.) / Lecture Notes in Computer Science; Vol. 1988. Springer, 2001. P. 544-551.

  170. J.J.H. Miller, A.P. Musgrave, G.I. Shishkin. A robust layer-resolving numerical method for plane stagnation point flow. In: Numerical Analysis and Its Applications: Second International Conference, NAA 2000, Rousse, Bulgaria, June 2000; Revised Papers, L.Vulkov, J.Wasniewski and P.Yalamov (Eds.) / Lecture Notes in Computer Science; Vol. 1988. Springer, 2001. P. 594-601.

  171. G.I. Shishkin. A posteriori and a priori techniques of local grid refinement for parabolic problems with boundary and transition layers. In: Numerical Analysis and Its Applications: Second International Conference, NAA 2000, Rousse, Bulgaria, June 2000; Revised Papers, L.Vulkov, J.Wasniewski and P.Yalamov (Eds.) / Lecture Notes in Computer Science; Vol. 1988. Springer, 2001. P. 710-722.

  172. G.I. Shishkin, P.A. Farrell, A.F. Hegarty, J.J.H. Miller, E. O'Riordan. On a necessary requirement for Re-uniform numerical methods to solve boundary layer equations for flow along a flat plate. In: Numerical Analysis and Its Applications: Second International Conference, NAA 2000, Rousse, Bulgaria, June 2000; Revised Papers, L.Vulkov, J.Wasniewski and P.Yalamov (Eds.) / Lecture Notes in Computer Science; Vol. 1988. Springer, 2001. P. 723-731.

  173. I.V. Tselishcheva, G.I. Shishkin. A domain decomposition finite difference method for singularly perturbed elliptic equations in composed domains. In: Numerical Analysis and Its Applications: Second International Conference, NAA 2000, Rousse, Bulgaria, June 2000; Revised Papers, L.Vulkov, J.Wasniewski and P.Yalamov (Eds.) / Lecture Notes in Computer Science; Vol. 1988. Springer, 2001. P. 756-763.

  174. J. Etienne, J.J.H. Miller, G.I. Shishkin. A robust layer-resolving numerical method for a free convection problem. In: Mathematics and the 21st Century: Proceedings of the International Conference, Cairo, Egypt, January 10-20, 2000, A. A. Ashour and A.-S. F. Obada eds., World Scientific, Singapore, 2001, P. 189-198.

  175. A.R. Ansari, A.F. Hegarty, G.I. Shishkin. Parameter-uniform numerical methods for a laminar jet problem. In: ECCOMAS Computational Fluid Dynamics Conference 2001, Swansea, Wales, UK, 4-7 September 2001. Proceedings in Adobe Acrobat format on CD Rom. - to appear in the International Journal for Numerical Methods in Fluids.

  176. J.A. Butler, J.J.H. Miller, G.I. Shishkin. A Reynolds-uniform numerical method for Prandtl's boundary layer problem for flow past a wedge. In: ECCOMAS Computational Fluid Dynamics Conference 2001, Swansea, Wales, UK, 4-7 September 2001. Proceedings in Adobe Acrobat format on CD Rom. - to appear in the International Journal for Numerical Methods in Fluids.

  177. P.A. Farrell, A.F. Hegarty, J.J.H. Miller, E. O'Riordan, G.I. Shishkin. Computing realistic Reynolds-uniform error bounds for discrete derivatives of flow velocities in the boundary layer for Prandtl's problem. In: ECCOMAS Computational Fluid Dynamics Conference 2001, Swansea, Wales, UK, 4-7 September 2001. Proceedings in Adobe Acrobat format on CD Rom. - to appear in the International Journal for Numerical Methods in Fluids.

  178. J.J.H. Miller, A.P. Musgrave, G.I. Shishkin. A Reynolds-uniform numerical method for the Prandtl solution and its derivatives for stagnation line flow. In: ECCOMAS Computational Fluid Dynamics Conference 2001, Swansea, Wales, UK, 4-7 September 2001. Proceedings in Adobe Acrobat format on CD Rom. - to appear in the International Journal for Numerical Methods in Fluids.

  179. I.V. Tselishcheva, G.I. Shishkin. On one singularly perturbed diffusion problem with a discontinuous convective term. In: Modern Problems of Mathematical Modelling, Proceedings of the IXth Russian School-Workshop, Durso, 17-22 September 2001. Rostov-na-Donu, 2001. P. 388-396 (in Russian).

    2002

  180. C. Clavero, J. L. Gracia, F. Lisbona, G. I. Shishkin. A robust method of improved order for convection-diffusion problems in a domain with characteristic boundaries. ZAMM - Z. angew. Math. Mech., 2002, 82 (9), 631-647.

  181. P.A. Farrell, A.F. Hegarty, J.J.H. Miller, E. O'Riordan, G.I. Shishkin. An experimental technique for computing parameter-uniform error estimates for numerical solutions of singular perturbation problems, with an application to Prandtl's problem at high Reynolds number. Applied Numerical Mathematics, 2002, 40 (1-4), 143-149   (A special issue "Papers from the III PanAmerican Workshop in Applied and Computational Mathematics", J. Castillo, V. Peryra and S. Steinberg eds.).

  182. P.W. Hemker, G.I. Shishkin, L.P. Shishkina. High-order time-accurate schemes for parabolic singular perturbation problems with convection. Russian J. Numer. Anal. Math. Modelling, 2002, 17 (1), 1-24.

  183. P.W. Hemker, G.I. Shishkin, L.P. Shishkina. High-order time-accurate schemes for singularly perturbed parabolic convection-diffusion problems with Robin boundary conditions. Computational Methods in Applied Mathematics, 2002, 2 (1), 3-25.

  184. H. Mac Mullen, E. O'Riordan, G.I. Shishkin. The convergence of classical Schwarz methods applied to convection-diffusion problems with regular boundary layers. Applied Numerical Mathematics, 2002, 43 (3), 297-313.

  185. S. Matthews, E. O'Riordan, G.I. Shishkin. A numerical method for a system of singularly perturbed reaction-diffusion equations. Journal of Computational and Applied Mathematics, 2002, 145 (1), 151-166.

  186. G.I. Shishkin. Grid approximations with an improved rate of convergence for singularly perturbed elliptic equations in domains with characteristic boundaries. Sib. Zh. Vychisl. Mat. (Sib. J. Numer. Math.), 2002, 5 (1), 71-92 (in Russian).

  187. G.I. Shishkin. Optimal, with respect to the order of the convergence rate, piecewise uniform grids for singularly perturbed convection-diffusion equations. Izv. Vyssh. Uchebn. Zaved. Mat., 2002, No. 3, 60-72 (in Russian).

  188. G.I. Shishkin. Grid approximation of a singularly perturbed parabolic reaction-diffusion equation with a fast-moving source. Zh. Vychisl. Mat. Mat. Fiz., 2002, 42 (6), 823-836 (in Russian); transl. in Comput. Maths. Math. Phys., 2002, 42 (6), 788-801.

  189. G.I. Shishkin. Grid approximation of solutions and derivatives in the case of singularly perturbed elliptic convection-diffusion equations. Dokl. Rus. Akad. Nauk, 2002, 384 (3), 312-315 (in Russian); English transl. in Doklady Mathematics, 2002, 65 (3), 373-376.

  190. G.I. Shishkin. Adaptive mesh method for a singularly perturbed parabolic equation with a moving concentrated source. Dokl. Rus. Akad. Nauk, 2002, 386 (1), 25-29 (in Russian); English transl. in Doklady Mathematics, 2002, 66 (2), 175-178.

  191. P.W. Hemker, G.I. Shishkin, L.P. Shishkina. High-order time-accurate schemes for parabolic singular perturbation convection-diffusion problems with Robin boundary conditions. In: Optimization of Finite Element Approximations & Splines and Wavelets, Proceedings of the 2-nd International Conference OFEA'2001, St. Petersburg, Russia, June 25-29, 2001. St. Petersburg, 2002. Volume 2. P. 32-48.

  192. G.I. Shishkin. Grid approximation of a singularly perturbed parabolic reaction-diffusion equation with a fast-moving source on a line. In: Optimization of Finite Element Approximations & Splines and Wavelets, Proceedings of the 2-nd International Conference OFEA'2001, St. Petersburg, Russia, June 25-29, 2001. St. Petersburg, 2002. Volume 2. P. 118-133 (in Russian).

  193. A.R. Ansari, G.I. Shishkin. A Reynolds-uniform numerical method for oscillating flow through a pipe. In: Proceedings of the International Conference on Computational Mathematics (Novosobirsk, June 2002), G.A. Mikhailov, V.P. Il'in and Yu.M. Laevsky eds. ICM&MG Publisher, 2002. Part II. P. 315-321.

  194. P.W. Hemker, G.I. Shishkin, L.P. Shishkina. Defect correction high-order accurate schemes for parabolic singularly perturbed convection-diffusion problems. In: Proceedings of the International Conference on Computational Mathematics (Novosobirsk, June 2002), G.A. Mikhailov, V.P. Il'in and Yu.M. Laevsky eds. ICM&MG Publisher, 2002. Part II. P. 454-459.

  195. P.W. Hemker, G.I. Shishkin, I.V. Tselishcheva. Parameter-uniform numerical methods for a class of quasilinear singularly perturbed convection-diffusion equations in a composed domain. In: Proceedings of the International Conference on Computational Mathematics (Novosobirsk, June 2002), G.A. Mikhailov, V.P. Il'in and Yu.M. Laevsky eds. ICM&MG Publisher, 2002. Part II. P. 460-466.

  196. H. Mac Mullen, G.I. Shishkin. An e-uniform discrete non-overlapping domain decomposition method for a singularly perturbed convection-diffusion problem. In: Proceedings of the International Conference on Computational Mathematics (Novosobirsk, June 2002), G.A. Mikhailov, V.P. Il'in and Yu.M. Laevsky eds. ICM&MG Publisher, 2002. Part II. P. 643-648.

  197. A.R. Ansari, B. Hossain, G.I. Shishkin. On numerical methods for a boundary layer on a body of revolution. In: Symmetry and Differential Equations 2002, Proceedings of the Third International conference (Krasnoyarsk, August 2002). P. 17-21.

  198. G.I. Shishkin. An adaptive mesh method for a singularly perturbed parabolic equation in a composed domain with a concentrated source on the moving interface boundary. In: Symmetry and Differential Equations 2002, Proceedings of the Third International conference (Krasnoyarsk, August 2002). P. 255-260.

  199. J.S. Butler, J.J.H.Miller, G.I. Shishkin. A Reynolds-uniform numerical method for Prandtl`s boundary layer problem for flow past a plate with mass transfer, in: Recent Advances in Computational Science & Engineering, Eds. H.P. Lee, K. Kumar, Imperial College Press, 2002, 733-737. - submitted to Journal of Computational Methods in Sciences and Engineering.

  200. R.K. Dunne, E. O'Riordan, G.I. Shishkin. Boundary layers in singularly perturbed problems on non-rectangular domains. In: Proceedings of BAIL 2002: An International Conference on Boundary and Interior Layers - Computational & Asymptotic Methods, Perth, Western Australia, 8th-12th July, 2002, S. Wang and N. Fowkes eds. The University of Western Australia, 2002. P. 109-114.

  201. P.A. Farrell, A.F. Hegarty, J.J.H. Miller, E. O'Riordan, G.I. Shishkin. Singularly perturbed convection-duffusion problems with boundary and week interior layers. In: Proceedings of BAIL 2002: An International Conference on Boundary and Interior Layers - Computational & Asymptotic Methods, Perth, Western Australia, 8th-12th July, 2002, S. Wang and N. Fowkes eds. The University of Western Australia, 2002. P. 115-120.

  202. P.A. Farrell, P.W. Hemker, G.I. Shishkin, L.P. Shishkina. Iterative domain decomposition methods for singularly perturbed nonlinear convection-duffusion equations. In: Proceedings of BAIL 2002: An International Conference on Boundary and Interior Layers - Computational & Asymptotic Methods, Perth, Western Australia, 8th-12th July, 2002, S. Wang and N. Fowkes eds. The University of Western Australia, 2002. P. 121-126.

  203. J.J.H. Miller, G.I. Shishkin, B. Koren, L.P. Shishkina. Grid approximation of a singularly perturbed boundary value problem modelling heat transfer in the case of flow over a flat plate with suction of the boundary layer. In: Proceedings of BAIL2002: An International Conference on Boundary and Interior Layers - Computational & Asymptotic Methods, Perth, Western Australia, 8th-12th July, 2002, S. Wang and N. Fowkes eds. The University of Western Australia, 2002. P. 13-22. - to appear in Journal of Computational Applied Mathematics.

  204. E. O'Riordan, G.I. Shishkin. Singularly perturbed parabolic problems with non-smooth data. In: Proceedings of BAIL2002: An International Conference on Boundary and Interior Layers - Computational & Asymptotic Methods, Perth, Western Australia, 8th-12th July, 2002, S. Wang and N. Fowkes eds. The University of Western Australia, 2002. P. 201-206.

  205. G.I. Shishkin. Limitations of adaptive mesh refinement techniques for singularly perturbed problems with a moving interior layer. In: Proceedings of BAIL2002: An International Conference on Boundary and Interior Layers - Computational & Asymptotic Methods, Perth, Western Australia, 8th-12th July, 2002, S. Wang and N. Fowkes eds. The University of Western Australia, 2002. P. 23-33.

  206. G.I. Shishkin. One concept in the approximation of solution and derivatives for singularly perturbed elliptic convection-diffusion equations. In: Proceedings of BAIL2002: An International Conference on Boundary and Interior Layers - Computational & Asymptotic Methods, Perth, Western Australia, 8th-12th July, 2002, S. Wang and N. Fowkes eds. The University of Western Australia, 2002. P. 221-226.

    2003

  207. A.R. Ansari, A.F. Hegarty, G.I. Shishkin. A note on fitted operator methods for a laminar jet problem, Applied Numerical Mathematics, 2003, 45 (4), 353-365.

  208. A.R. Ansari, A.F. Hegarty, G.I. Shishkin. Parameter-uniform numerical methods for a laminar jet problem, International Journal for Numerical Methods in Fluids, 2003, 43 (8), 937-952.

  209. J.A. Butler, J.J.H. Miller, G.I. Shishkin. A Reynolds-uniform numerical method for Prandtl's boundary layer problem for flow past a wedge, International Journal for Numerical Methods in Fluids, 2003, 43 (8), 903-914.

  210. R.K. Dunne, E. O'Riordan, G.I. Shishkin. A fitted mesh method for a class of singularly perturbed parabolic problems with a boundary turning point, Computational Methods in Applied Mathematics, 2003, 3 (3), 361-372.

  211. P.A. Farrell, A.F. Hegarty, J.J.H. Miller, E. O'Riordan, G.I. Shishkin. Computing realistic Reynolds-uniform error bounds for discrete derivatives of flow velocities in the boundary layer for Prandtl's problem, International Journal for Numerical Methods in Fluids, 2003, 43 (8). P. 895-902.

  212. P.A. Farrell, A.F. Hegarty, J.J.H. Miller, E. O'Riordan, G.I. Shishkin. Numerical techniques for flow problems with singularities, International Journal for Numerical Methods in Fluids, 2003, 43 (8), 915-936.

  213. P.W. Hemker, G.I. Shishkin, L.P. Shishkina. Novel defect-correction high-order, in space and time, accurate schemes for parabolic singularly perturbed convection-diffusion problems, Computational Methods in Applied Mathematics, 2003, 3 (3), 387-404.

  214. P.W. Hemker, G.I. Shishkin, L.P. Shishkina. High-order time-accurate schemes for parabolic singular perturbation convection-diffusion problems with Robin boundary conditions, Mat. Model., 2003, 15 (8), 99-112 (in Russian).

  215. B. Hossain, A.R. Ansari, G.I. Shishkin. On numerical methods for a boundary layer on a body of revolution, Computational Methods in Applied Mathematics, 2003, 3 (3), 405-416.

  216. J.J.H. Miller, A.P. Musgrave, G.I. Shishkin. A Reynolds-uniform numerical method for the Prandtl solution and its derivatives for stagnation line flow, International Journal for Numerical Methods in Fluids, 2003, 43 (8), 881-894.

  217. E. O'Riordan, M.L. Pickett, G.I. Shishkin. Singularly perturbed problems modeling reaction-convection-diffusion equations, Computational Methods in Applied Mathematics, 2003, 3 (3), 424-442.

  218. G.I. Shishkin. On conditioning of a Schwarz method for singularly perturbed convection-diffusion equations in the case of disturbances in the data of the boundary value problem, Computational Methods in Applied Mathematics, 2003, 3 (3), 459-487.

  219. G.I. Shishkin. Approximation of solutions and derivatives for singularly perturbed elliptic convection-diffusion equations, Mathematical Proceedings of the Royal Irish Academy, 2003, 103A (2), 169-201.

  220. G.I. Shishkin. Grid approximation of a singularly perturbed one-dimensional heat equation on an unbounded domain excluding a rectangle with sides noncollinear to the axes, Russian J. Numer. Analysis and Math. Modelling, 2003, 18 (5), 429-454.

  221. G.I. Shishkin. Numerical methods on adaptive meshes for singularly perturbed elliptic equations in a domain with a curvilinear boundary, Izv. Vyssh. Uchebn. Zaved. Mat., 2003, no. 1, 74-85 (in Russian).

  222. G.I. Shishkin. Grid approximation of elliptic convection-diffusion equations in an unbounded domain with boundary layers of different types, Dokl. Rus. Akad. Nauk, 2003, 392 (4), 452-456 (in Russian); English transl. in Doklady Mathematics, 2003, 68 (2), 234-238.

  223. G.I. Shishkin. Schwarz grid method for singularly perturbed convection-diffusion parabolic equations in the case of coherent and incoherent meshes on subdomains. Zh. Vychisl. Mat. Mat. Fiz., 2003, 43 (2), 261-274 (in Russian); transl. in Comput. Maths. Math. Phys., 2003, 43 (2), 242-254.

  224. G.I. Shishkin. Approximation of solutions and derivatives for a singularly perturbed elliptic convection-diffusion equation, Zh. Vychisl. Mat. Mat. Fiz., 2003, 43 (5), 671-687 (in Russian); transl. in Comput. Maths. Math. Phys., 2003, 43 (5), 641-657.

  225. G.I. Shishkin. Grid approximation of a singularly perturbed parabolic equation on a composed domain with a moving interface containing a concentrated source, Zh. Vychisl. Mat. Mat. Fiz., 2003, 43 (12), 1806-1824 (in Russian); transl. in Comput. Maths. Math. Phys., 2003, 43 (12), 1738-1755.

  226. G.I. Shishkin. Grid approximation of a singularly perturbed parabolic reaction-diffusion equation with a moving concentrated source, Mat. Model., 2003, 15 (2), 43-61 (in Russian).

  227. G.I. Shishkin. Grid approximation of improved convergence order for a singularly perturbed elliptic convection-diffusion equation, Proceedings of the Steklov Institute of Mathematics, 2003, Suppl. 1, pp. S184-S202; Translated from Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2003, Vol. 9, No. 1.

  228. G.I. Shishkin. An improved piecewise uniform mesh for a singularly perturbed elliptic reaction-diffusion equation, Proceedings of the Steklov Institute of Mathematics, 2003, Suppl. 2, pp. S138-S147; Translated from Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2003, Vol. 9, No. 1.

    2004

  229. P.W. Hemker, G.I. Shishkin, L.P. Shishkina. High-order accurate decomposition of Richardson's method for a singularly perturbed elliptic reaction-diffusion equation, Zh. Vychisl. Mat. Mat. Fiz., 2004, 44 (2), 328-336; transl. in Comp. Math. Math. Phys., 2004, 44 (2), 309-316.

  230. P.A. Farrell, A.F. Hegarty, J.J.H. Miller, E. O'Riordan, G.I. Shishkin. Singularly perturbed convection-diffusion problems with boundary and weak interior layers, Journal of Computational and Applied Mathematics, 2004, 166 (1), 133-151.

  231. J.J.H. Miller, G.I. Shishkin, B. Koren, L.P. Shishkina. Grid approximation of a singularly perturbed boundary value problem modelling heat transfer in the case of flow over a flat plate with suction of the boundary layer, Journal of Computational and Applied Mathematics, 2004, 166 (1), 221-232.

  232. E. O'Riordan, G.I. Shishkin. Singularly perturbed parabolic problems with non-smooth data, Journal of Computational and Applied Mathematics, 2004, 166 (1), 233-245.

  233. G.I. Shishkin. Discrete approximations of solutions and derivatives for a singularly perturbed parabolic convection-diffusion equation, Journal of Computational and Applied Mathematics, 2004, 166 (1), 247-266.

  234. G.I. Shishkin. Limitations of adaptive mesh refinement techniques for singularly perturbed problems with a moving interior layer // Journal of Computational and Applied Mathematics, 2004, 166 (1), 267-280.

  235. G.I. Shishkin. Domain decomposition method in the case of non-overlapping subdomains for a singularly perturbed convection-diffusion equation. Izv. Vyssh. Uchebn. Zaved. Mat., 2004, no. 5 (in Russian) - to appear.


Recent Reports

  1. P.A. Farrell, A.F. Hegarty, J.J.H. Miller, E. O'Riordan E., G.I. Shishkin. A technique for computing realistic values of the error parameters for the numerical solutions of singular perturbation problems. TCDMATH Report Series, the School of Mathematics, Trinity College, Dublin. Preprint TCDMATH 99-06 (1999).

  2. P.A. Farrell, A.F. Hegarty, J.J.H. Miller, E. O'Riordan E., G.I. Shishkin. The e-uniform convergence of the discrete derivatives for singularly perturbed problems. TCDMATH Report Series, the School of Mathematics, Trinity College, Dublin. Preprint TCDMATH 99-07 (1999).

  3. P.A. Farrell, A.F. Hegarty, J.J.H. Miller, E. O'Riordan E., G.I. Shishkin. Numerical analysis of Re-uniform convergence for boundary layer equations for a flat plate. TCDMATH Report Series, the School of Mathematics, Trinity College, Dublin. Preprint TCDMATH 99-08 (1999).

  4. P.A. Farrell, A.F. Hegarty, J.J.H. Miller, E. O'Riordan E., G.I. Shishkin. An iterative Re-uniform method for the numerical solution of the Prandtl boundary-layer problem. TCDMATH Report Series, the School of Mathematics, Trinity College, Dublin. Preprint TCDMATH 99-11 (1999).

  5. G.I. Shishkin. Discrete approximation of the Riemann problem for the viscous Burgers equation. TCDMATH Report Series, School of Mathematics, Trinity College, Dublin. Preprint TCDMATH 99-12 (1999).

  6. J. Etienne, J.J.H. Miller, G.I. Shishkin. A robust layer-resolving numerical method for a free convection problem. TCDMATH Report Series, the School of Mathematics, Trinity College, Dublin. Preprint TCDMATH 00-03 (2000).

  7. B. Gahan, J.J.H. Miller, G.I. Shishkin. Accurate numerical method for Blasius' problem for flow past a flat plate with mass transfer. TCDMATH Report Series, the School of Mathematics, Trinity College, Dublin. Preprint TCDMATH 00-05 (2000).

  8. P.A. Farrell, A.F. Hegarty, J.J.H. Miller, E. O'Riordan E., G.I. Shishkin. An experimental technique for computing parameter-uniform error estimates for numerical solutions of singular perturbation problems, with an application to Prandtl's problem at high Reynolds number. TCDMATH Report Series, the School of Mathematics, Trinity College, Dublin. Preprint TCDMATH 00-06 (2000).

  9. B. Gahan, J.J.H. Miller, G.I. Shishkin. Reynolds-uniform numerical method for Prandtl's problem with suction-blowing based on Blasius' approach. TCDMATH Report Series, the School of Mathematics, Trinity College, Dublin. Preprint TCDMATH 00-07 (2000).

  10. S. Matthews, J.J.H. Miller, E. O'Riordan, G.I. Shishkin. A parameter robust numerical method for a system of singularly perturbed ordinary differential equations. DCU Maths. Dept. Preprint Series, Dublin City University. Preprint MS-00-03 (2000).

  11. H. MacMulen, E. O'Riordan, G.I. Shishkin. Schwarz methods for convection-diffusion problems. DCU Maths. Dept. Preprint Series, Dublin City University. Preprint MS-00-04 (2000).

  12. R.K. Dunne, E. O'Riordan, G.I. Shishkin. Singularly perturbed parabolic problems on non-rectangular domains. DCU Maths. Dept. Preprint Series, Dublin City University. Preprint MS-00-05 (2000).

  13. S. Matthews, E. O'Riordan, G.I. Shishkin. Numerical methods for a system of singularly perturbed reaction-diffusion equations. DCU Maths. Dept. Preprint Series, Dublin City University. Preprint MS-00-06 (2000).

  14. P.A. Farrell, A.F. Hegarty, J.J.H. Miller, E. O'Riordan, G.I. Shishkin. Parameter-uniform numerical methods for a class of singularly perturbed problems with a Neumann boundary condition. DCU Maths. Dept. Preprint Series, Dublin City University. Preprint MS-00-11 (2000).

  15. P.W. Hemker, G.I. Shishkin, L.P. Shishkina. High-order time-accurate schemes for parabolic singular perturbation problems with convection. CWI Research Reports. Modelling, Analysis and Simulation (MAS) Report Series. Preprint MAS-R0101 (2001).

  16. P.A. Farrell, J.J.H. Miller, E. O'Riordan, G.I. Shishkin. Parameter-uniform fitted mesh method for quasilinear differential equations with boundary layers. DCU Maths. Dept. Preprint Series, Dublin City University. Preprint MS-01-01 (2001).

  17. H. MacMullen, E. O'Riordan, G.I. Shishkin. The convergence of classical Schwarz methods applied to convection-diffusion problems with regular boundary layers. DCU Maths. Dept. Preprint Series, Dublin City University.
    Preprint MS-01-02 (2001).

  18. P.A. Farrell, A.F. Hegarty, J.J.H. Miller, E. O'Riordan, G.I. Shishkin. Global maximum norm parameter-uniform numerical method for a singularly perturbed convection-diffusion problem with discontinuous convection coefficient. DCU Maths. Dept. Preprint Series, Dublin City University. Preprint MS-01-06 (2001).

  19. P.A. Farrell, A.F. Hegarty, J.J.H. Miller, E. O'Riordan, G.I. Shishkin. Singularly perturbed convection diffusion problems with boundary and weak interior layers. DCU Maths. Dept. Preprint Series, Dublin City University. Preprint MS-01-07 (2001).

  20. R.K. Dunne, E. O'Riordan, G.I. Shishkin. A fitted mesh method for a class of singularly perturbed parabolic problems with a boundary turning point. DCU Maths. Dept. Preprint Series, Dublin City University. Preprint MS-01-10 (2001).

  21. G.I Shishkin. Approximations of solutions and derivatives for singularly perturbed elliptic convection-diffusion equations. TCDMATH Report Series, the School of Mathematics, Trinity College, Dublin. Preprint TCDMATH 01-16 (2001).

  22. P.W. Hemker, G.I. Shishkin, L.P. Shishkina. High-order time-accurate schemes for singularly perturbed parabolic convection-diffusion problems with Robin boundary conditions. CWI Research Reports. Modelling, Analysis and Simulation (MAS) Report Series. Preprint MAS-R0207 (2002).

  23. P.W. Hemker, G.I. Shishkin, L.P. Shishkina. High-Order accurate decomposition methods based on Richardson's extrapolation for a singularly perturbed elliptic reaction-diffusion equation on a strip. TCDMATH Report Series, the School of Mathematics, Trinity College, Dublin. Preprint TCDMATH 02-04 (2002).

  24. J.J.H. Miller, G.I. Shishkin, L.P. Shishkina, B. Koren. Grid approximation of a singularly perturbed boundary value problem modelling heat transfer in the case of flow over a flat plate with suction of the boundary layer. TCDMATH Report Series, the School of Mathematics, Trinity College, Dublin. Preprint TCDMATH 02-01 (2002).

  25. G.I. Shishkin. Limitations of adaptive mesh refinement methods for a singularly perturbed parabolic equation in a composed domain with a concentrated source on the moving interface boundary. TCDMATH Report Series, the School of Mathematics, Trinity College, Dublin. Preprint TCDMATH 02-02 (2002).

  26. J.J.H. Miller, R.E. O'Malley, G.I. Shishkin. Grid approximation of multiscale problems arising in singularly perturbed parabolic reaction-diffusion equations in an unbounded domain. TCDMATH Report Series, the School of Mathematics, Trinity College, Dublin. Preprint TCDMATH 02-05 (2002).

  27. E. O'Riordan, G.I. Shishkin. Singularly perturbed parabolic problems with non-smooth data. DCU Maths. Dept. Preprint Series, Dublin City University. Preprint MS-02-06 (2002).

  28. G.I. Shishkin. On conditioning of a Schwarz method for singularly perturbed convection--diffusion equations in the case of disturbances in the data of the boundary value problem. TCDMATH Report Series, the School of Mathematics, Trinity College Dublin. Preprint TCDMATH 03-01 (2003).

  29. G.I. Shishkin. Improved e-uniform accurate schemes for singularly perturbed elliptic convection-diffusion 3D problems. The Richardson extrapolation technique. TCDMATH Report Series, the School of Mathematics, Trinity College Dublin. Preprint TCDMATH 03-08 (2003).

  30. P.W. Hemker, G.I. Shishkin, and L.P. Shishkina. Domain decomposition method for a singularly perturbed quasilinear parabolic convection-diffusion equation. TCDMATH Report Series, the School of Mathematics, Trinity College Dublin. Preprint TCDMATH 03-02 (2003).

  31. P.W. Hemker, G.I. Shishkin, L.P. Shishkina. Improved e-uniform accurate schemes for singularly perturbed parabolic convection-diffusion problems. Defect-correction technique. TCDMATH Report Series, the School of Mathematics, Trinity College Dublin. Preprint TCDMATH 03-07 (2003).

  32. P.A. Farrell, A.F. Hegarty, J.J.H. Miller, E. O'Riordan, G.I. Shishkin. Numerical techniques for flow problems with singularities. TCDMATH Report Series, the School of Mathematics, Trinity College Dublin. Preprint TCDMATH 03-03 (2003).

  33. J.S. Butler, J.J.H Miller, G.I. Shishkin. A Reynolds-uniform numerical method for Prandtl's boundary layer problem for flow past a wedge. TCDMATH Report Series, the School of Mathematics, Trinity College Dublin. Preprint TCDMATH 03-05 (2003).

  34. J.S. Butler, J.J.H Miller, G.I. Shishkin. A Reynolds-uniform numerical method for Prandtl's boundary layer problem for flow past a plate with mass transfer. TCDMATH Report Series, the School of Mathematics, Trinity College Dublin. Preprint TCDMATH 03-06 (2003).

  35. A.R. Ansari, J.J.H. Miller, G.I. Shishkin. Robust numerical method for periodic driven flow through a pipe. ULMS Report Series, Department of Mathematics & Statistics, University of Limerick, Ireland. Preprint ULMS-03-01 (2003).

  36. P.A. Farrell, E. O'Riordan, G.I. Shishkin. A class of singularly perturbed semilinear differential equations with interior layers. Mathematical Sciences Preprint Series, Dublin City University. Preprint MS-03-08 (2003).



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