Publications  of  Grigorii  Shishkin

      Number of papers:  170+
   Number of communications to scientific meetings:  70+
   Number of books:   4  


Selected Papers

  1. G.I. Shishkin. A certain heat problem with a free boundary. Dokl. Akad. Nauk SSSR, 1971, v. 197, 1276-1279 (in Russian); transl. in Soviet Math. Dokl., 1971, v. 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), 89-92, Banach Center Publ., 3, PWN, Warsaw, 1978 (in Russian).

  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. N.N. Krasovskii, S.I. Tarasova, V.E. Tret'jakov, G.I. Shishkin. Control with information deficit. Problems Control Inform. Theory (Problemy Upravlen. Teor. Inform.), 1986, 15 (3), 203-218.

  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. 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).

  16. 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).

  17. 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.

  18. 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.

  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. Math. Phys., 1988, 28 (6), 32-41.

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

  21. 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), 320-325, Boole Press Conf. Ser., 12, Boole, Dun Laoghaire, 1988.

  22. 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.

  23. 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.

  24. 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.

  25. 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.

  26. 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.

  27. 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.

  28. 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.

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

  30. G.I. Shishkin. Grid approximation of a singularly perturbed elliptic equation; the case of a reduced equation of zero order that is degenerate on the boundary. Numerical methods and software (Russian), 140-163, Akad. Nauk SSSR, Otdel Vychisl. Mat., Moscow, 1990 (in Russian).

  31. I.V. Pershin, V.A. Titov, G.I. Shishkin. Approximation of solutions of parabolic equations with a rapidly moving source. Control in dynamical systems (Russian), 85-92, Akad. Nauk SSSR, Ural. Otdel., Sverdlovsk, 1990 (in Russian).

  32. V.E. Tret'yakov, G.I. Shishkin. Stochastic programs in control problems under an information deficit. Control in dynamical systems (Russian), 101-115, Akad. Nauk SSSR, Ural. Otdel., Sverdlovsk, 1990 (in Russian).

  33. 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.

  34. 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.

  35. 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.

  36. 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).

  37. 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).

  38. 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.

  39. 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.

  40. 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.

  41. G.I. Shishkin. Difference approximation of a singularly perturbed boundary value problem for quasilinear elliptic equations that degenerate 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.

  42. G.I. Shishkin. A difference scheme for a singularly perturbed parabolic equation that is degenerate 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.

  43. 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.

  44. 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.

  45. I.V. Pershin, V.A. Titov, G.I. Shishkin. Approximation of solutions of heat equations for rapid processes in moving media. Control problems with guaranteed result (Russian), 52-65, Ross. Akad. Nauk, Ural. Otdel., Ekaterinburg, 1992 (in Russian).

  46. V.E. Tret'yakov, I.V. Tselishcheva, G.I. Shishkin. On an efficient algorithm in control problems with an information deficit. Control problems with guaranteed result (Russian), 104-114, Ross. Akad. Nauk, Ural. Otdel., Ekaterinburg, 1992 (in Russian).

  47. V.E. Tret'yakov, I.V. Tselishcheva, G.I. Shishkin. Optimal control of systems with incomplete and inexact information. Proceedings of the Institute of Mathematics and Mechanics, Vol. 2, 176-187, Ross. Akad. Nauk, Ural. Otdel., Inst. Mat. Mekh., Ekaterinburg, 1992 (in Russian).

  48. G.I. Shishkin. Grid approximation of a singularly perturbed boundary value problem for quasilinear parabolic equations in the case of complete degeneration with respect to space variables. Numerical methods and mathematical modeling (Russian), 103-128, Ross. Akad. Nauk, Inst. Vychisl. Mat., Moscow, 1992 (in Russian).

  49. 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.

  50. 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.

  51. 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.

  52. G.I. Shishkin. Grid approximation of the Dirichlet problem for a singularly perturbed quasilinear parabolic equation with 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.

  53. 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.

  54. G.I. Shishkin. Grid approximation of singularly perturbed quasilinear elliptic equations that degenerate to 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.

  55. 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.

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

  57. 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.

  58. 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.

  59. 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. Appl. Numer. Methods., 1994, 10, 297-302.

  60. 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.

  61. 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.

  62. 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, 1993), eds D.Bainov and V.Covachev. International Science Publishers, 1994, 83-92.

  63. 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.

  64. 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.

  65. 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.

  66. 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. Differ. Uravneniya, 1994, 30 (7), 1244-1258 (in Russian); transl. in Differential Equations, 1994, 30 (7), 1152-1166.

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

  68. 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.

  69. 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.

  70. 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, 47-54.

  71. 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.

  72. 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.

  73. 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).

  74. 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.

  75. 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).

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

  77. 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).

  78. 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.

  79. 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).

  80. 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.

  81. 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.

  82. 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.

  83. 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.

  84. 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.

  85. 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.

  86. 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.

  87. 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.

  88. 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.

  89. 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.

  90. 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.

  91. 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).

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

  93. 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.

  94. 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.

  95. 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.

  96. 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.

  97. 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.

  98. 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.

  99. 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.

  100. 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.

  101. 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.

  102. 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, 4, 98-107 (in Russian); transl. in Russian Math. (Izv. VUZ), 1997, 41 (4), 96-105.

  103. 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.

  104. 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.

  105. 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.

  106. 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.

  107. 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.

  108. 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.

  109. 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.

  110. 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.

  111. 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.

  112. 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.

  113. G.I. Shishkin. Grid approximation of the problem of the decay of a discontinuity 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.

  114. 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.

  115. G.I. Shishkin. Grid approximations for 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.

  116. 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.

  117. 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.

  118. 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.

  119. 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.

  120. 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.

  121. J.J.H. Miller, E. O'Riordan and G.I. Shishkin. Fitted numerical methods for four simple convection-diffusion problems. Proc. of the Second Asian Conference on Numerical Analysis, Thailand 1995, S. Tangmanee and E. Schulz eds., World Scientific, 1998, 444-448.

  122. 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.

  123. 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.

  124. G.I. Shishkin. Increasing the accuracy of approximate solutuions 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.

  125. 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.

  126. 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).

  127. 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).

  128. 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.

  129. 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.

  130. 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.

  131. 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.

  132. 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.

  133. 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.

  134. 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.

  135. 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.

  136. 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.

  137. 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.

  138. 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.

  139. 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.

  140. 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.

  141. 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) (in Russian); transl. in Comp. Math. Math. Phys., 2000, 40 (5), 680-691.

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

  143. 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.

  144. 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 (J.J.H. Miller, G.I. Shishkin and L.Vulkov eds.), Nova Science, N.Y., 2000. P. 23-32.

  145. 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 (J.J.H. Miller, G.I. Shishkin and L.Vulkov eds.), Nova Science, N.Y., 2000. P. 33-42.

  146. 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 (J.J.H. Miller, G.I. Shishkin and L.Vulkov eds.), Nova Science, N.Y., 2000. P. 43-50.

  147. 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 (J.J.H. Miller, G.I. Shishkin and L.Vulkov eds.), Nova Science, N.Y., 2000. P. 219-224.

  148. 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 (J.J.H. Miller, G.I. Shishkin and L.Vulkov eds.), Nova Science, N.Y., 2000. P. 213-218.

  149. 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 (J.J.H. Miller, G.I. Shishkin and L.Vulkov eds.), Nova Science, N.Y., 2000. P. 111-121.

  150. 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 (J.J.H. Miller, G.I. Shishkin and L.Vulkov eds.), Nova Science, N.Y., 2000. P. 251-257.

  151. 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.

  152. 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.

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

  154. 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).

  155. G.I. Shishkin. Grid approximation of the wave equation singularly perturbed with respect to the spatial variable. Izv. Vyssh. Uchebn. Zaved. Mat., 2001, 1, 66-81 (in Russian).

  156. 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.

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


Recent Reports

  1. H. MacMullen, J.J.H. Miller, E. O'Riordan, G.I.Shishkin. A second order parameter-robust overlapping Schwartz method for reaction-diffusion problems with boundary layers. INCA Preprint No. 1, November 1997.

  2. 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, Ireland. Preprint TCDMATH 99-06 (1999).

  3. 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, Ireland. Preprint TCDMATH 99-07 (1999).

  4. 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, Ireland. Preprint TCDMATH 99-08 (1999).

  5. 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, Ireland. Preprint TCDMATH 99-11 (1999).

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

  7. 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, Ireland. Preprint TCDMATH 00-03 (2000).

  8. 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, Ireland. Preprint TCDMATH 00-05 (2000).

  9. 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, Ireland. Preprint TCDMATH 00-06 (2000).

  10. 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, Ireland. Preprint TCDMATH 00-07 (2000).

  11. 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-00-003 (2000).

  12. H. MacMulen, E. O'Riordan, G.I. Shishkin. Schwarz methods for convection-diffusion problems. DCU Maths. Dept. Preprint Series, Dublin City University. Preprint MS-00-004 (2000).

  13. 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-00-005 (2000).

  14. 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-00-006 (2000).

  15. 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-00-011 (2000).

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

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, Singapore, 1996. xiv + 166 pp.

  3. P.A. Farrell, A.F. Hegarty, J.J.H. Miller, E. O'Riordan, G.I. Shishkin. Robust Computational Techniques for Boundary Layers. Chapman and Hall / CRC Press, Boca Raton, U.S.A., 2000. 256 pp.

  4. J.J.H. Miller, G.I. Shishkin, L.G. Vulkov (Eds.). Analytical and Numerical Methods for Convection-Dominated and Singularly Perturbed Problems. Nova Science Publishers, Inc., N.Y., 2000. 400 pp. approx. (published in Oct.-Nov. 2000)

Updated on February 8, 2001 by Irina Tselishcheva

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