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Makarov Vladimir Leonidovich

Publications in Math-Net.Ru

  1. New implementation of the FD-method for Sturm–Liouville problems with Dirichlet–Neumann boundary conditions

    Tr. Inst. Mat., 22:1 (2014),  98–106
  2. A Two-Sided Functional-Discrete Method for Second-Order Differential Equations with General Boundary Conditions

    Differ. Uravn., 40:7 (2004),  964–977
  3. A functional difference method for solving left-definite Sturm–Liouville problems with an eigenparameter in the boundary conditions

    Zh. Vychisl. Mat. Mat. Fiz., 42:5 (2002),  676–689
  4. Sufficient conditions for the eigenvalues of the operator $-d^2/dx^2+q(x)$ under the Ionkin–Samarskii conditions

    Zh. Vychisl. Mat. Mat. Fiz., 40:12 (2000),  1787–1800
  5. A two-sided FD-method for solving the Dirichlet problem for the Helmholtz equation

    Differ. Uravn., 35:3 (1999),  388–395
  6. Sufficient conditions for the convergence of nonclassical asymptotic expansions for the Sturm–Liouville problem with periodic conditions

    Differ. Uravn., 35:3 (1999),  367–378
  7. Accurate three-point difference schemes for second-order nonlinear ordinary differential equations and their implementation

    Zh. Vychisl. Mat. Mat. Fiz., 39:1 (1999),  45–60
  8. Analysis of structures based on graded semiconductor compound

    Mat. Model., 10:11 (1998),  63–81
  9. A two-sided functional-discrete method for solving boundary value problems for second-order ordinary differential equations

    Differ. Uravn., 33:7 (1997),  955–962
  10. Difference schemes of a high-order of accuracy for degenerate systems of differential equations on nonuniform grids

    Differ. Uravn., 33:3 (1997),  410–415
  11. Raising the accuracy of approximations of polynomial operators in Hilbert spaces by the interpolation method

    Dokl. Akad. Nauk, 334:1 (1994),  20–22
  12. A three-point difference scheme of a high order of accuracy for a system of second-order ordinary differential equations (the nonselfadjoint case)

    Differ. Uravn., 30:3 (1994),  493–502
  13. FD-schemes of any order of accuracy (uniform with respect to $\epsilon$) for singularly perturbed systems of second-order ordinary differential equations with piecewise-smooth coefficients

    Differ. Uravn., 30:2 (1994),  292–301
  14. The Cayley transform and the solution of an initial value problem for a first order differential equation with an unbounded operator coefficient in Hilbert space

    Mat. Model., 6:6 (1994),  94–107
  15. Polynomial interpolation of operators in vector spaces

    Dokl. Akad. Nauk, 329:2 (1993),  135–139
  16. Spectral properties of the Laplace difference operator on a hexagonal grid, and some of their applications

    Differ. Uravn., 29:7 (1993),  1216–1221
  17. Hermitian interpolation of operators in Hilbert spaces

    Dokl. Akad. Nauk, 327:2 (1992),  183–186
  18. Polynomial interpolation of operators in Hilbert spaces

    Dokl. Akad. Nauk, 324:4 (1992),  742–745
  19. Stability and convergence of difference schemes in Chebyshev norm for parabolic equation with nonlocal boundary condition

    Mat. Model., 4:4 (1992),  63–73
  20. Polynomial interpolation of nonlinear functionals

    Dokl. Akad. Nauk SSSR, 321:3 (1991),  470–473
  21. A functional-difference method of arbitrary order of accuracy for solving the Sturm–Liouville problem with piecewise-smooth coefficients

    Dokl. Akad. Nauk SSSR, 320:1 (1991),  34–39
  22. On the general structure of polynomial functional interpolants

    Dokl. Akad. Nauk SSSR, 318:4 (1991),  805–808
  23. A mathematical model of a varyzone semiconductor diode with re-emission

    Zh. Vychisl. Mat. Mat. Fiz., 31:6 (1991),  887–900
  24. Exact three-point difference schemes for second-order nonlinear ordinary differential equations and their realization

    Dokl. Akad. Nauk SSSR, 312:4 (1990),  795–800
  25. Realization of exact three-point difference schemes for second-order ordinary differential equations with piecewise smooth coefficients

    Dokl. Akad. Nauk SSSR, 312:3 (1990),  538–543
  26. Realization of exact three-point difference schemes for second-order ordinary differential equations with piecewise-smooth coefficients

    Differ. Uravn., 26:7 (1990),  1254–1265
  27. An interpolation formula of Newton type for nonlinear functionals

    Dokl. Akad. Nauk SSSR, 307:3 (1989),  534–537
  28. Accuracy of a difference scheme for quasilinear elliptic equations in a rhombus with solutions in the class $W_2^k(\Omega)$, $1<k\le4$

    Differ. Uravn., 25:7 (1989),  1240–1249
  29. An interpolation method for solving the identification problem for a function system described by the Uryson operator

    Dokl. Akad. Nauk SSSR, 300:6 (1988),  1332–1336
  30. Estimates for the rate of convergence of the difference approximation of the Dirichlet problem for the equation $-\Delta u+\sum_{|\alpha|\le1}(-1)^{|\alpha|}D^\alpha q_\alpha(x)u=f(x)$ for $q_\alpha(x)\in W_\infty^{\lambda|\alpha|}(\Omega)$, $\lambda\in(0,1]$

    Differ. Uravn., 24:11 (1988),  1987–1994
  31. Convergence of difference solutions to generalized solutions of the first boundary value problem for a fourth-order elliptic operator in domains of arbitrary form

    Differ. Uravn., 23:8 (1987),  1403–1407
  32. An estimate for the rate of convergence of a difference scheme in the$L_2$-norm for the third boundary value problem of axisymmetric elasticity theory on solutions in $W_2^1(\Omega)$

    Differ. Uravn., 23:7 (1987),  1207–1219
  33. Compatible convergence-rate estimates of the mesh method for the axisymmetric Poisson equation in spherical coordinates

    Zh. Vychisl. Mat. Mat. Fiz., 27:8 (1987),  1252–1255
  34. Matched estimates of the rate of convergence of the net method for Poisson's equation in polar coordinates

    Zh. Vychisl. Mat. Mat. Fiz., 27:6 (1987),  867–874
  35. Consistent estimates for the rate of convergence of difference schemes in $L_2$-norm for the third boundary value problem of elasticity theory

    Differ. Uravn., 22:7 (1986),  1265–1268
  36. Exact difference schemes for a class of nonlinear boundary value problems and their application

    Differ. Uravn., 22:7 (1986),  1155–1165
  37. The accuracy of difference schemes in the class of generalized solutions of an elliptic equation with variable coefficients in an arbitrary convex domain

    Differ. Uravn., 22:6 (1986),  1046–1054
  38. The rate of convergence of a difference scheme using the sum approximation method for generalized solutions

    Zh. Vychisl. Mat. Mat. Fiz., 26:6 (1986),  941–946
  39. On the accuracy of the method of lines for second-order quasilinear hyperbolic equations with a small parameter multiplying the highest time derivative

    Differ. Uravn., 21:7 (1985),  1164–1170
  40. Solution of a boundary value problem for a quasilinear equation of parabolic type with nonclassical boundary condition

    Differ. Uravn., 21:2 (1985),  296–305
  41. Exact and truncated difference schemes for boundary value problems with degeneration

    Differ. Uravn., 21:2 (1985),  285–295
  42. Difference schemes in discrete $L_2$-space for a class of problems with nonlinear boundary condition

    Izv. Vyssh. Uchebn. Zaved. Mat., 1985, no. 10,  31–38
  43. Estimation of the rate of convergence of difference schemes for quasilinear fourth order elliptic equations

    Zh. Vychisl. Mat. Mat. Fiz., 25:11 (1985),  1725–1729
  44. The convergence of difference solutions to the generalized solutions of the Dirichlet problem for the Helmholtz equation in a convex polygon

    Zh. Vychisl. Mat. Mat. Fiz., 25:9 (1985),  1336–1345
  45. Estimation of the accuracy of the method of summary approximation of the solution of an abstract Cauchy problem

    Dokl. Akad. Nauk SSSR, 275:2 (1984),  297–301
  46. Exact and truncated difference schemes for a fourth-order ordinary differential equation

    Differ. Uravn., 20:9 (1984),  1502–1514
  47. On an estimate of the rate of convergence of difference solutions to generalized solutions of the Dirichlet problem for the Helmholtz equation in a convex polygon

    Dokl. Akad. Nauk SSSR, 273:5 (1983),  1040–1044
  48. Consistent estimates for the rate of convergence of the method of nets for quasilinear equations of elliptic type with large Lipschitz constant

    Differ. Uravn., 19:7 (1983),  1246–1250
  49. Convergence of difference schemes for elliptic equations with mixed derivatives and generalized solutions

    Differ. Uravn., 19:7 (1983),  1140–1145
  50. Consistent estimates of the rate of convergence of difference solutions to generalized solutions of the first boundary value problem for fourth-order equations

    Izv. Vyssh. Uchebn. Zaved. Mat., 1983, no. 2,  15–22
  51. Applicability of the method of nets and the method of lines to the solution of a class of problems of optimal control theory

    Zh. Vychisl. Mat. Mat. Fiz., 23:4 (1983),  798–805
  52. Convergence of difference solutions to generalized solutions of the Dirichlet problem for the Helmholtz equation in an arbitrary domain

    Dokl. Akad. Nauk SSSR, 267:1 (1982),  34–37
  53. Difference schemes of second-order precision for the axially symmetric Poisson equation on generalized solutions in $W_2^2$

    Dokl. Akad. Nauk SSSR, 262:1 (1982),  22–26
  54. The accuracy of the method of nets in eigenvalue problems

    Differ. Uravn., 18:7 (1982),  1240–1244
  55. The rate of convergence for the method of nets for a Sturm–Liouville problem with a generalized differential Hermitian operator

    Differ. Uravn., 18:7 (1982),  1167–1172
  56. Application of exact difference schemes to the construction and study of difference schemes for generalized solutions

    Mat. Sb. (N.S.), 117(159):4 (1982),  469–480
  57. An algorithm for constructing completely conservative difference schemes

    Zh. Vychisl. Mat. Mat. Fiz., 22:1 (1982),  123–132
  58. Convergence of a difference method and the method of lines for multidimensional problems of mathematical physics in classes of generalized solutions

    Dokl. Akad. Nauk SSSR, 259:2 (1981),  282–286
  59. On the method of nets for the Sturm–Liouville problem with a generalized differential Hermite operator

    Differ. Uravn., 17:7 (1981),  1239–1249
  60. Difference schemes of any order of accuracy for second-order differential equations on the half-axis

    Differ. Uravn., 17:3 (1981),  527–540
  61. A difference scheme of second-order accuracy for an axisymmetric Poisson equation on generalized solutions

    Zh. Vychisl. Mat. Mat. Fiz., 21:5 (1981),  1168–1179
  62. An approach to testing the adequacy of the flow chart of the algorithm of functioning of the structure scheme of a pulse information measuring system

    Dokl. Akad. Nauk SSSR, 255:1 (1980),  36–40
  63. On estimating the rate of convergence of difference schemes in eigenvalue problems for convex domains

    Dokl. Akad. Nauk SSSR, 254:5 (1980),  1035–1038
  64. On the question of the convergence rate of truncated schemes of the $m$th rank for generalized solutions

    Differ. Uravn., 16:7 (1980),  1276–1282
  65. Exact and truncated difference schemes for a class of Sturm–Liouville problems with degeneration

    Differ. Uravn., 16:7 (1980),  1265–1275
  66. Application of exact difference schemes to the estimation of the rate of convergence for the method of lines

    Zh. Vychisl. Mat. Mat. Fiz., 20:2 (1980),  371–387
  67. A completely conservative difference scheme for equations of gas dynamics in Euler variables

    Zh. Vychisl. Mat. Mat. Fiz., 20:1 (1980),  171–181
  68. A variant of the method of fictitious domains in eigenvalue problems

    Differ. Uravn., 15:9 (1979),  1676–1680
  69. Exact difference schemes and schemes of any order of accuracy for systems of second-order differential equations

    Differ. Uravn., 15:7 (1979),  1194–1205
  70. On the adequacy of mathematical simulation of a complex information and measuring system

    Dokl. Akad. Nauk SSSR, 240:2 (1978),  287–290
  71. The construction of particular solutions of resonance differential equations

    Differ. Uravn., 14:7 (1978),  1255–1261
  72. Turing machines and finite automata

    Sibirsk. Mat. Zh., 5:1 (1964),  102–108

  73. Lyudmila Filippovna Zelikina

    Differ. Uravn., 35:6 (1999),  848–849
  74. Theory of difference schemes: A. A. Samarskii, 656 p. “Nauka”, Moscow, 1977. Book review

    Zh. Vychisl. Mat. Mat. Fiz., 18:4 (1978),  1062–1063

© Steklov Math. Inst. of RAS, 2026