Shishkin Grigorii Ivanovich

Publications in Math-Net.Ru

1. Richardson’s third-order difference scheme for the Cauchy problem in the case of transport equation
   
   Zh. Vychisl. Mat. Mat. Fiz., 64:10 (2024),  1826–1835
2. An improved difference scheme for the Cauchy problem in the case of a transport equation
   
   Zh. Vychisl. Mat. Mat. Fiz., 63:8 (2023),  1272–1278
3. A difference scheme of the decomposition method for an initial boundary value problem for the singularly perturbed transport equation
   
   Zh. Vychisl. Mat. Mat. Fiz., 62:7 (2022),  1224–1232
4. Erratum to: Monotone decomposition of the Cauchy problem for a hyperbolic equation based on transport equations
   
   Zh. Vychisl. Mat. Mat. Fiz., 62:4 (2022),  700
5. Monotone decomposition of the Cauchy problem for a hyperbolic equation based on transport equations
   
   Zh. Vychisl. Mat. Mat. Fiz., 62:3 (2022),  442–450
6. Difference scheme for an initial-boundary value problem for a singularly perturbed transport equation
   
   Zh. Vychisl. Mat. Mat. Fiz., 57:11 (2017),  1824–1830
7. Computer difference scheme for a singularly perturbed elliptic convection-diffusion equation in the presence of perturbations
   
   Zh. Vychisl. Mat. Mat. Fiz., 57:5 (2017),  814–831
8. Computer difference scheme for a singularly perturbed reaction-diffusion equation in the presence of perturbations
   
   Model. Anal. Inform. Sist., 23:5 (2016),  577–586
9. Difference scheme of highest accuracy order for a singularly perturbed reaction-diffusion equation based on the solution decomposition method
   
   Trudy Inst. Mat. i Mekh. UrO RAN, 21:1 (2015),  280–293
10. Difference scheme for a singularly perturbed parabolic convection–diffusion equation in the presence of perturbations
    
    Zh. Vychisl. Mat. Mat. Fiz., 55:11 (2015),  1876–1892
11. A higher order accurate solution decomposition scheme for a singularly perturbed parabolic reaction-diffusion equation
    
    Zh. Vychisl. Mat. Mat. Fiz., 55:3 (2015),  393–416
12. A stable standard difference scheme for a singularly perturbed convection-diffusion equation in the presence of computer perturbations
    
    Trudy Inst. Mat. i Mekh. UrO RAN, 20:1 (2014),  322–333
13. Computer difference scheme for a singularly perturbed convection-diffusion equation
    
    Zh. Vychisl. Mat. Mat. Fiz., 54:8 (2014),  1256–1269
14. Conditioning and stability of finite difference schemes on uniform meshes for a singularly perturbed parabolic convection-diffusion equation
    
    Zh. Vychisl. Mat. Mat. Fiz., 53:4 (2013),  575–599
15. Conditioning of a difference scheme of the solution decomposition method for a singularly perturbed convection-diffusion equation
    
    Trudy Inst. Mat. i Mekh. UrO RAN, 18:2 (2012),  291–304
16. Strong stability of a scheme on locally uniform meshes for a singularly perturbed ordinary differential convection–diffusion equation
    
    Zh. Vychisl. Mat. Mat. Fiz., 52:6 (2012),  1010–1041
17. A finite difference scheme of improved accuracy on a priori adapted grids for a singularly perturbed parabolic convection–diffusion equation
    
    Zh. Vychisl. Mat. Mat. Fiz., 51:10 (2011),  1816–1839
18. Improved approximations of the solution and derivatives to a singularly perturbed reaction-diffusion equation based on the solution decomposition method
    
    Zh. Vychisl. Mat. Mat. Fiz., 51:6 (2011),  1091–1120
19. Improved difference scheme of the solution decomposition method for a singularly perturbed reaction-diffusion equation
    
    Trudy Inst. Mat. i Mekh. UrO RAN, 16:1 (2010),  255–271
20. A Richardson scheme of the decomposition method for solving singularly perturbed parabolic reaction-diffusion equation
    
    Zh. Vychisl. Mat. Mat. Fiz., 50:12 (2010),  2113–2133
21. A conservative difference scheme for a singularly perturbed elliptic reaction-diffusion equation: approximation of solutions and derivatives
    
    Zh. Vychisl. Mat. Mat. Fiz., 50:4 (2010),  665–678
22. A Richardson scheme of an increased order of accuracy for a semilinear singularly perturbed elliptic convection-diffusion equation
    
    Zh. Vychisl. Mat. Mat. Fiz., 50:3 (2010),  458–478
23. Approximation of singularly perturbed parabolic equations in unbounded domains subject to piecewise smooth boundary conditions in the case of solutions that grow at infinity
    
    Zh. Vychisl. Mat. Mat. Fiz., 49:10 (2009),  1827–1843
24. The Richardson scheme for the singularly perturbed parabolic reaction-diffusion equation in the case of a discontinuous initial condition
    
    Zh. Vychisl. Mat. Mat. Fiz., 49:8 (2009),  1416–1436
25. Finite difference schemes for the singularly perturbed reaction-diffusion equation in the case of spherical symmetry
    
    Zh. Vychisl. Mat. Mat. Fiz., 49:5 (2009),  840–856
26. Sequential and parallel domain decomposition methods for a singularly perturbed parabolic convection-diffusion equation
    
    Trudy Inst. Mat. i Mekh. UrO RAN, 14:1 (2008),  202–220
27. Grid approximation of a parabolic convection-diffusion equation on a priori adapted grids: $\varepsilon$-uniformly convergent schemes
    
    Zh. Vychisl. Mat. Mat. Fiz., 48:6 (2008),  1014–1033
28. Conditioning of finite difference schemes for a singularly perturbed convection-diffusion parabolic equation
    
    Zh. Vychisl. Mat. Mat. Fiz., 48:5 (2008),  813–830
29. Approximation of a system of singularly perturbed reaction-diffusion parabolic equations in a rectangle
    
    Zh. Vychisl. Mat. Mat. Fiz., 48:4 (2008),  660–673
30. Grid approximation of singularly perturbed parabolic equations with piecewise continuous initial-boundary conditions
    
    Trudy Inst. Mat. i Mekh. UrO RAN, 13:2 (2007),  218–233
31. Grid approximation of a singularly perturbed quasilinear parabolic convection-diffusion equation on a priori adapted meshes
    
    Kazan. Gos. Univ. Uchen. Zap. Ser. Fiz.-Mat. Nauki, 149:4 (2007),  146–172
32. Necessary conditions for $\varepsilon$-uniform convergence of finite difference schemes for parabolic equations with moving boundary layers
    
    Zh. Vychisl. Mat. Mat. Fiz., 47:10 (2007),  1706–1726
33. Approximation of systems of singularly perturbed elliptic reaction-diffusion equations with two parameters
    
    Zh. Vychisl. Mat. Mat. Fiz., 47:5 (2007),  835–866
34. Approximation of the solution and its derivative for the singularly perturbed Black–Scholes equation with nonsmooth initial data
    
    Zh. Vychisl. Mat. Mat. Fiz., 47:3 (2007),  460–480
35. Richardson's method for increasing the accuracy of difference solutions of singularly perturbed elliptic convection-diffusion equations
    
    Izv. Vyssh. Uchebn. Zaved. Mat., 2006, no. 2,  57–71
36. Higher-order accurate method for a quasilinear singularly perturbed elliptic convection-diffusion equation
    
    Sib. Zh. Vychisl. Mat., 9:1 (2006),  81–108
37. Grid approximation of singularly perturbed parabolic reaction-diffusion equations on large domains with respect to the space and time variables
    
    Zh. Vychisl. Mat. Mat. Fiz., 46:11 (2006),  2045–2064
38. The use of solutions on embedded grids for the approximation of singularly perturbed parabolic convection-diffusion equations on adapted grids
    
    Zh. Vychisl. Mat. Mat. Fiz., 46:9 (2006),  1617–1637
39. Grid approximation of singularly perturbed parabolic equations in the presence of weak and strong transient layers induced by a discontinuous right-hand side
    
    Zh. Vychisl. Mat. Mat. Fiz., 46:3 (2006),  407–420
40. A method of asymptotic constructions of improved accuracy for a quasilinear singularly perturbed parabolic convection-diffusion equation
    
    Zh. Vychisl. Mat. Mat. Fiz., 46:2 (2006),  242–261
41. Grid approximation of singularly perturbed parabolic convection-diffusion equations with a piecewise-smooth initial condition
    
    Zh. Vychisl. Mat. Mat. Fiz., 46:1 (2006),  52–76
42. A Higher-Order Richardson Method for a Quasilinear Singularly Perturbed Elliptic Reaction-Diffusion Equation
    
    Differ. Uravn., 41:7 (2005),  980–989
43. A domain decomposition method in the case of nonoverlapping subdomains for a singularly perturbed convection-diffusion equation
    
    Izv. Vyssh. Uchebn. Zaved. Mat., 2005, no. 2,  62–73
44. On an adaptive grid method for singularly perturbed elliptic reaction-diffusion equations in a domain with a curvilinear boundary
    
    Izv. Vyssh. Uchebn. Zaved. Mat., 2005, no. 1,  73–88
45. Grid approximation of the domain and solution decomposition method with improved convergence rate for singularly perturbed elliptic equations in domains with characteristic boundaries
    
    Zh. Vychisl. Mat. Mat. Fiz., 45:7 (2005),  1196–1212
46. Grid approximation in a half plane for singularly perturbed elliptic equations with convective terms that grow at infinity
    
    Zh. Vychisl. Mat. Mat. Fiz., 45:2 (2005),  298–314
47. Grid approximation of a singularly perturbed elliptic equation with convective terms in the presence of various boundary layers
    
    Zh. Vychisl. Mat. Mat. Fiz., 45:1 (2005),  110–125
48. High-order accurate decomposition of the Richardson method for a singularly perturbed elliptic reaction-diffusion equation
    
    Zh. Vychisl. Mat. Mat. Fiz., 44:2 (2004),  329–337
49. Numerical methods on adaptive grids for singularly perturbed elliptic equations in a domain with a curvilinear boundary
    
    Izv. Vyssh. Uchebn. Zaved. Mat., 2003, no. 1,  74–85
50. High-order time-accurate schemes for parabolic singular perturbation convection-diffusion problems with Robin boundary conditions
    
    Mat. Model., 15:8 (2003),  99–112
51. Grid approximation for a singularly perturbed parabolic reaction-diffusion equation with a moving concentrated source
    
    Mat. Model., 15:2 (2003),  43–61
52. An improved piecewise uniform mesh for a singularly perturbed elliptic reaction-diffusion equation
    
    Trudy Inst. Mat. i Mekh. UrO RAN, 9:2 (2003),  172–179
53. Grid approximation of improved convergence order for a singularly perturbed elliptic convection-diffusion equation
    
    Trudy Inst. Mat. i Mekh. UrO RAN, 9:1 (2003),  165–182
54. The grid approximation of a singularly perturbed parabolic equation on a composed domain with a moving boundary containing a concentrated source
    
    Zh. Vychisl. Mat. Mat. Fiz., 43:12 (2003),  1806–1824
55. Approximation of solutions and derivative of singularly perturbed elliptic equation of convection-diffusion
    
    Zh. Vychisl. Mat. Mat. Fiz., 43:5 (2003),  672–689
56. The Schwarz grid method for singularly perturbed convection-diffusion parabolic equations in the case of coherent and incoherent grids on subdomains
    
    Zh. Vychisl. Mat. Mat. Fiz., 43:2 (2003),  251–264
57. Piecewise-uniform grids, optimal with respect to the order of convergence, for singularly perturbed convection-diffusion equations
    
    Izv. Vyssh. Uchebn. Zaved. Mat., 2002, no. 3,  60–72
58. Grid approximations with an improved rate of convergence for singularly perturbed elliptic equations in domains with characteristic boundaries
    
    Sib. Zh. Vychisl. Mat., 5:1 (2002),  71–92
59. Grid approximation of a singularly perturbed parabolic reaction-diffusion equation with a fast-moving source
    
    Zh. Vychisl. Mat. Mat. Fiz., 42:6 (2002),  823–836
60. Grid Approximations to Singularly Perturbed Parabolic Equations with Turning Points
    
    Differ. Uravn., 37:7 (2001),  987–999
61. A Grid Approximation to the Transport Equation in the Problem on a Flow Past a Flat Plate at Large Reynolds Numbers
    
    Differ. Uravn., 37:3 (2001),  415–424
62. Grid approximation of a wave equation singularly perturbed with respect to the space variable
    
    Izv. Vyssh. Uchebn. Zaved. Mat., 2001, no. 1,  67–81
63. The method of total approximation for singularly perturbed elliptic equations with convective terms
    
    Mat. Model., 13:4 (2001),  95–108
64. Approximation of singularly perturbed reaction-diffusion equations on adaptive meshes
    
    Mat. Model., 13:3 (2001),  103–118
65. Monotone difference schemes for equations with mixed derivative
    
    Mat. Model., 13:2 (2001),  17–26
66. A decomposition method for singularly perturbed parabolic convectiondiffusion equations with discontinuous initial conditions
    
    Sib. Zh. Vychisl. Mat., 4:1 (2001),  85–106
67. Mesh approximation of singularly perturbed equations with convective terms for the perturbation of data
    
    Zh. Vychisl. Mat. Mat. Fiz., 41:5 (2001),  692–707
68. Grid approximation of the solution to the Blasius equation and of its derivatives
    
    Zh. Vychisl. Mat. Mat. Fiz., 41:1 (2001),  39–56
69. Distributing the numerical solution of parabolic singularly perturbed problems with defect correction over independent processes
    
    Sib. Zh. Vychisl. Mat., 3:3 (2000),  229–258
70. Approximation of systems of convection-diffusion elliptic equations with parabolic boundary layers
    
    Zh. Vychisl. Mat. Mat. Fiz., 40:11 (2000),  1648–1661
71. Grid approximation of singularly perturbed boundary value problems on locally condensing grids: Convection-diffusion equations
    
    Zh. Vychisl. Mat. Mat. Fiz., 40:5 (2000),  714–725
72. Optimization of piecewise-uniform grids for singularly perturbed equations of reaction-diffusion type
    
    Differ. Uravn., 35:7 (1999),  990–997
73. 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
74. Grid approximation of singularly perturbed boundary value problems on locally refined meshes. Reaction-diffusion equations
    
    Mat. Model., 11:12 (1999),  87–104
75. Grid approximation of singularly perturbed boundary value problems in a nonconvex domain with a piecewise smooth boundary
    
    Mat. Model., 11:11 (1999),  75–90
76. Singularly perturbed boundary value problems with locally perturbed initial conditions: Equations with convective terms
    
    Zh. Vychisl. Mat. Mat. Fiz., 39:2 (1999),  262–279
77. Grid approximation of singularly perturbed systems of elliptic and parabolic equations with convective terms
    
    Differ. Uravn., 34:12 (1998),  1686–1696
78. Grid approximations of singularly perturbed systems for parabolic convection-diffusion equations with counterflow
    
    Sib. Zh. Vychisl. Mat., 1:3 (1998),  281–297
79. Finite-difference approximations for singularly perturbed elliptic equations
    
    Zh. Vychisl. Mat. Mat. Fiz., 38:12 (1998),  1989–2001
80. 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., 38:11 (1998),  1844–1859
81. A grid approximation for the Riemann problem in the case of the Burgers equation
    
    Zh. Vychisl. Mat. Mat. Fiz., 38:8 (1998),  1418–1420
82. The decomposition method for singularly perturbed boundary value problems with the local perturbation of the initial conditions. Equations with convective terms
    
    Izv. Vyssh. Uchebn. Zaved. Mat., 1997, no. 4,  98–107
83. Singularly perturbed boundary value problems with concentrated sources and discontinuous initial conditions
    
    Zh. Vychisl. Mat. Mat. Fiz., 37:4 (1997),  429–446
84. Grid approximation of a singularly perturbed Neumann problem for parabolic equations in the case of a discontinuous boundary function
    
    Zh. Vychisl. Mat. Mat. Fiz., 37:3 (1997),  378–381
85. Grid approximation of singularly perturbed equations with convective terms in the case of mixed boundary conditions
    
    Differ. Uravn., 32:5 (1996),  689–701
86. Grid approximation of singularly perturbed quasi-linear elliptic equations in a case of multiple solutions of the reduced equation
    
    Mat. Model., 8:7 (1996),  109–127
87. Parallel methods of solving singularly perturbed boundary value problems for elliptic equations
    
    Mat. Model., 8:3 (1996),  111–127
88. Approximation of the solutions and diffusion flows of singularly perturbed boundary-value problems with discontinuous initial conditions
    
    Zh. Vychisl. Mat. Mat. Fiz., 36:9 (1996),  83–104
89. Grid approximation of parabolic equations with singular initial conditions
    
    Zh. Vychisl. Mat. Mat. Fiz., 36:3 (1996),  73–92
90. Locally one-dimensional difference schemes for singularly perturbed parabolic equations
    
    Zh. Vychisl. Mat. Mat. Fiz., 36:2 (1996),  42–61
91. A difference scheme for the problem of the decay of a discontinuity in the case of the viscous Burgers equation
    
    Dokl. Akad. Nauk, 342:3 (1995),  313–317
92. Difference schemes on locally condensing grids
    
    Differ. Uravn., 31:7 (1995),  1179–1183
93. Grid approximation of quasi-linear singularly perturbed elliptic and parabolic equations with mixed boundary conditions
    
    Mat. Model., 7:10 (1995),  111–126
94. A problem for grid approximation of the diffusion flow in numerical modelling of pollution transport
    
    Mat. Model., 7:7 (1995),  61–80
95. Experimental evaluation of the order of uniform convergence for special difference schemes
    
    Mat. Model., 7:6 (1995),  85–94
96. Grid approximation of boundary value problems for singularly perturbed quasi-linear elliptic equations with interior layer
    
    Mat. Model., 7:2 (1995),  72–88
97. Mesh approximation of singularly perturbed boundary-value problems for systems of elliptic and parabolic equations
    
    Zh. Vychisl. Mat. Mat. Fiz., 35:4 (1995),  542–564
98. Grid approximation of boundary value problems for singularly perturbed quasilinear elliptic equations in the case of limit equations that are degenerate on the boundary
    
    Differ. Uravn., 30:7 (1994),  1244–1258
99. Grid approximation of singularly perturbed equations, degenerated on the boundary. The case of sharply changing coefficients in the neighbourhood of the boundary layer
    
    Mat. Model., 6:5 (1994),  105–121
100. The method of additive separation of singularities for quasilinear singularly perturbed elliptic and parabolic equations
     
     Zh. Vychisl. Mat. Mat. Fiz., 34:12 (1994),  1793–1814
101. A grid approximation of singularly perturbed quasilinear elliptic and parabolic equations which degenerate into equations without spatial derivatives
     
     Zh. Vychisl. Mat. Mat. Fiz., 34:11 (1994),  1632–1651
102. A grid approximation of the method of additive separation of singularities for a singularly perturbed equation of parabolic type
     
     Zh. Vychisl. Mat. Mat. Fiz., 34:5 (1994),  720–738
103. Grid approximation of the Dirichlet problem for a singularly perturbed quasilinear parabolic equation with a transition layer
     
     Dokl. Akad. Nauk, 332:4 (1993),  424–427
104. Grid approximation of a singularly perturbed quasilinear equation with a transition layer
     
     Dokl. Akad. Nauk, 328:3 (1993),  299–302
105. Mesh approximation of singularly perturbed quasilinear elliptic equations which degenerate to a zero-order equation
     
     Zh. Vychisl. Mat. Mat. Fiz., 33:9 (1993),  1305–1323
106. Lattice approximation of singularly perturbed degenerate elliptic equations
     
     Zh. Vychisl. Mat. Mat. Fiz., 33:4 (1993),  541–560
107. The optimal control of systems with incomplete and incorrect information
     
     Trudy Inst. Mat. i Mekh. UrO RAN, 2 (1992),  176–187
108. A difference scheme for a singularly perturbed parabolic equation degenerating on the boundary
     
     Zh. Vychisl. Mat. Mat. Fiz., 32:5 (1992),  717–732
109. A difference approximation of a singularly perturbed boundary-value problem for quasilinear elliptic equations degenerating into first-order equations
     
     Zh. Vychisl. Mat. Mat. Fiz., 32:4 (1992),  550–566
110. Difference approximation of a singularly perturbed quasilinear elliptic equation that degenerates into a first-order equation
     
     Dokl. Akad. Nauk SSSR, 317:4 (1991),  845–849
111. The mathematical modelling of hydrogen diffusion process in welding joints with inclusions
     
     Mat. Model., 3:3 (1991),  27–35
112. Grid approximation of a singularly perturbed boundary-value problem for a quasi-linear elliptic equation in the completely degenerate case
     
     Zh. Vychisl. Mat. Mat. Fiz., 31:12 (1991),  1808–1825
113. A grid approximation of singularly perturbed parabolic equations degenerate on the boundary
     
     Zh. Vychisl. Mat. Mat. Fiz., 31:10 (1991),  1498–1511
114. A difference scheme for a singularly perturbed equation of parabolic type with discontinuous coefficients and concentrated factors
     
     Zh. Vychisl. Mat. Mat. Fiz., 29:9 (1989),  1277–1290
115. Approximation of solutions of singularly perturbed boundary value problems with a parabolic boundary layer
     
     Zh. Vychisl. Mat. Mat. Fiz., 29:7 (1989),  963–977
116. A difference scheme for a singularly perturbed equation of parabolic type with a discontinuous initial condition
     
     Dokl. Akad. Nauk SSSR, 300:5 (1988),  1066–1070
117. A difference scheme for a singularly perturbed equation of parabolic type with discontinuous boundary conditions
     
     Zh. Vychisl. Mat. Mat. Fiz., 28:11 (1988),  1649–1662
118. Approximation of the solutions of singularly perturbed boundary value problems with a corner boundary layer
     
     Dokl. Akad. Nauk SSSR, 296:1 (1987),  39–43
119. Approximation of solutions of singularly perturbed boundary-value problems with a corner boundary layer
     
     Zh. Vychisl. Mat. Mat. Fiz., 27:9 (1987),  1360–1374
120. A difference scheme for an elliptic equation with a small parameter multiplying the highest derivatives
     
     Dokl. Akad. Nauk SSSR, 286:1 (1986),  57–61
121. Solution of a boundary value problem for an elliptic equation with small parameter multiplying the highest derivatives
     
     Zh. Vychisl. Mat. Mat. Fiz., 26:7 (1986),  1019–1031
122. A difference scheme for a fourth-order elliptic equation with a small parameter multiplying the derivatives
     
     Differ. Uravn., 21:12 (1985),  2159–2165
123. A difference scheme for a fourth-order ordinary differential equation with a small parameter multiplying the highest derivative
     
     Differ. Uravn., 21:10 (1985),  1734–1742
124. A difference scheme for a fourth-order differential equation with a small parameter multiplying the highest derivative
     
     Dokl. Akad. Nauk SSSR, 275:6 (1984),  1323–1326
125. Increasing the accuracy of solutions of difference schemes for parabolic equations with a small parameter multiplying the highest derivative
     
     Zh. Vychisl. Mat. Mat. Fiz., 24:6 (1984),  864–875
126. Difference scheme on a nonuniform grid for a differential equation with small parameter multiplying the highest derivative
     
     Zh. Vychisl. Mat. Mat. Fiz., 23:3 (1983),  609–619
127. The numerical solution of elliptic equations with a small parameter at the leading derivatives
     
     Dokl. Akad. Nauk SSSR, 245:4 (1979),  804–808
128. Mesh method for solving elliptic equations with discontinuous boundary conditions
     
     Zh. Vychisl. Mat. Mat. Fiz., 19:3 (1979),  640–651
129. 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., 18:6 (1978),  1466–1475
130. The first boundary value problem for a second order equation with small parameters multiplying the derivatives
     
     Differ. Uravn., 13:2 (1977),  376–378
131. Über ein Problem Stefanschen Typs mit Verschwinden einer der Phasen
     
     Differ. Uravn., 12:12 (1976),  2283–2284
132. On a problem of Stefan type with discontinuous moving boundary
     
     Dokl. Akad. Nauk SSSR, 224:6 (1975),  1276–1278
133. On a heat transfer problem with free boundary
     
     Dokl. Akad. Nauk SSSR, 197:6 (1971),  1276–1279