All Stories

  1. Weighted Estimates for Boundary Value Problems with Fractional Derivatives

    Article • Computational Methods in Applied Mathematics, October 2020, De Gruyter

    Volodymyr Makarov, Dr. Nataliya Mayko, Ivan Gavrilyuk

  2. Exponentially convergent symbolic algorithm of the functional-discrete method for the fourth order Sturm–Liouville problems with polynomial coefficients

    Article • Journal of Computational and Applied Mathematics, March 2019, Elsevier

    Nataliia Romaniuk, Volodymyr Makarov

  3. An efficient approach for solving stiff nonlinear boundary value problems

    Article • Journal of Computational and Applied Mathematics, January 2019, Elsevier

    Volodymyr Makarov

  4. Exact and Approximate Solutions of Spectral Problems for the Schrödinger Operator on (−∞, ∞) with Polynomial Potential

    Article • Ukrainian Mathematical Journal, June 2018, Springer Science + Business Media

    Volodymyr Makarov

  5. Abstract Interpolating Fraction of the Thiele Type

    Article • Journal of Mathematical Sciences, May 2018, Springer Science + Business Media

    Volodymyr Makarov

  6. The Boundary Effect in the Accuracy Estimate for the Grid Solution of the Fractional Differential Equation

    Article • Computational Methods in Applied Mathematics, March 2018, De Gruyter

    Volodymyr Makarov, Dr. Nataliya Mayko

  7. Abstract Interpolation by Continued Thiele-Type Fractions

    Article • Cybernetics and Systems Analysis, January 2018, Springer Science + Business Media

    Volodymyr Makarov

  8. Symbolic Algorithm of the Functional-Discrete Method for a Sturm–Liouville Problem with a Polynomial Potential

    Article • Computational Methods in Applied Mathematics, October 2017, De Gruyter

    Nataliia Romaniuk, Volodymyr Makarov

  9. Super-Exponentially Convergent Parallel Algorithm for a Fractional Eigenvalue Problem of Jacobi-Type

    Article • Computational Methods in Applied Mathematics, June 2017, De Gruyter

    Ivan Gavrilyuk, Nataliia Romaniuk, Volodymyr Makarov

  10. Yurii Oleksiiovych Mitropol’skii (03.01.1917–14.06.2008), Outstanding Mathematician and Mechanician (on the 100th Anniversary of His Birth)

    Article • Ukrainian Mathematical Journal, June 2017, Springer Science + Business Media

    Volodymyr Makarov

  11. Exponentially Convergent Method For An Abstract Nonlocal Problem With Integral Nonlinearity

    Article • Ukrainian Mathematical Journal, May 2017, Springer Science + Business Media

    Volodymyr Makarov

  12. Weight Estimates of the Accuracy of Difference Schemes for the Sturm–Liouville Problem

    Article • Journal of Mathematical Sciences, February 2017, Springer Science + Business Media

    Volodymyr Makarov

  13. Superexponentially Convergent Algorithm for an Abstract Eigenvalue Problem with Applications to Ordinary Differential Equations

    Article • Journal of Mathematical Sciences, December 2016, Springer Science + Business Media

    Nataliia Romaniuk, Volodymyr Makarov

  14. Interpolating Integral Continued Fraction of the Thiele Type

    Article • Journal of Mathematical Sciences, November 2016, Springer Science + Business Media

    Volodymyr Makarov

  15. Exact and truncated difference schemes for boundary-value problem

    Article • January 2016, De Gruyter

    Volodymyr Makarov

  16. Super-Exponentially Convergent Parallel Algorithm for Eigenvalue Problems with Fractional Derivatives

    Article • Computational Methods in Applied Mathematics, January 2016, De Gruyter

    Prof. Ihor I. Demkiv, Volodymyr Makarov

  17. Exponentially Convergent Method for the First-Order Differential Equation in a Banach Space with Integral Nonlocal Condition

    Article • Ukrainian Mathematical Journal, January 2015, Springer Science + Business Media

    Volodymyr Makarov

  18. Existence of the solution to a nonlocal-in-time evolutional problem

    Article • Nonlinear Analysis Modelling and Control, September 2014, Vilnius University Press

    Volodymyr Makarov

  19. Algorithmic Aspects of Software Realization of the FD-method for the Solution of the Nonlinear Klein–Gordon Equation

    Article • Journal of Mathematical Sciences, January 2014, Springer Science + Business Media

    Volodymyr Makarov

  20. On the interpolation of a function on a bounded domain by its traces on parametric hypersurfaces

    Article • International Journal of Computer Mathematics, January 2014, Taylor & Francis

    Volodymyr Makarov

  21. An exponentially convergent functional-discrete method for solving Sturm–Liouville problems with a potential including the Dirac δ -function

    Article • Journal of Computational and Applied Mathematics, October 2013, Elsevier

    Volodymyr Makarov

  22. Anatolii Mykhailovych Samoilenko (on his 75th birthday)

    Article • Ukrainian Mathematical Journal, June 2013, Springer Science + Business Media

    Volodymyr Makarov

  23. FD-method for solving the nonlinear klein–gordon equation

    Article • Ukrainian Mathematical Journal, March 2013, Springer Science + Business Media

    Volodymyr Makarov

  24. Stability and Regularization of Difference Schemes in Banach and Hilbert Spaces

    Article • Computational Methods in Applied Mathematics, January 2013, De Gruyter

    Volodymyr Makarov

  25. The FD-method for solving Sturm-Liouville problems with special singular differential operator

    Article • Mathematics of Computation, August 2012, American Mathematical Society (AMS)

    Volodymyr Makarov

  26. Approximation of the Urysohn operator by operator polynomials of Stancu type

    Article • Ukrainian Mathematical Journal, August 2012, Springer Science + Business Media

    Volodymyr Makarov

  27. Compact difference schemes of high-order accuracy

    Article • Journal of Mathematical Sciences, April 2012, Springer Science + Business Media

    Volodymyr Makarov

  28. Exponentially Convergent Functional-discrete Method for Eigenvalue Transmission Problems with a Discontinuous Flux and the Potential as a Function in the Space L_1

    Article • Computational Methods in Applied Mathematics, January 2012, De Gruyter

    Volodymyr Makarov

  29. Exact and Truncated Difference Schemes for Boundary Value ODEs

    Article • January 2011, Springer Science + Business Media

    Volodymyr Makarov

  30. Introduction

    Article • January 2011, Springer Science + Business Media

    Volodymyr Makarov

  31. Exponentially Convergent Algorithms for Abstract Differential Equations

    Article • January 2011, Springer Science + Business Media

    Volodymyr Makarov

  32. The first-order equations

    Article • January 2011, Springer Science + Business Media

    Volodymyr Makarov

  33. Preliminaries

    Article • January 2011, Springer Science + Business Media

    Volodymyr Makarov

  34. The second-order equations

    Article • January 2011, Springer Science + Business Media

    Volodymyr Makarov

  35. Exercises and solutions

    Article • January 2011, Springer Science + Business Media

    Volodymyr Makarov

  36. A numerical-analytic method for solving the Cauchy problem for ordinary differential equations

    Article • Computational Methods in Applied Mathematics, January 2011, De Gruyter

    Volodymyr Makarov

  37. Difference schemes for nonlinear BVPs on the half-axis

    Article • January 2011, Springer Science + Business Media

    Volodymyr Makarov

  38. Three-point difference schemes for systems of monotone second-order ODEs

    Article • January 2011, Springer Science + Business Media

    Volodymyr Makarov

  39. Two-point difference schemes for systems of nonlinear BVPs

    Article • January 2011, Springer Science + Business Media

    Volodymyr Makarov

  40. Introduction and a short historical overview

    Article • January 2011, Springer Science + Business Media

    Volodymyr Makarov

  41. Three-point difference schemes for monotone second-order ODEs

    Article • January 2011, Springer Science + Business Media

    Volodymyr Makarov

  42. On continual interpolation nodes for operators in linear topological spaces

    Article • Ukrainian Mathematical Journal, October 2010, Springer Science + Business Media

    Volodymyr Makarov

  43. Two-point difference schemes of an arbitrary given order of accuracy for nonlinear BVPs

    Article • Applied Mathematics Letters, May 2010, Elsevier

    Volodymyr Makarov

  44. Exponentially Convergent Method for them-Point Nonlocal Problem for a First Order Differential Equation in Banach Space

    Article • Numerical Functional Analysis and Optimization, February 2010, Taylor & Francis

    Volodymyr Makarov

  45. Relation between interpolating integral continued fractions and interpolating branched continued fractions

    Article • Journal of Mathematical Sciences, February 2010, Springer Science + Business Media

    Volodymyr Makarov

  46. Adaptive algorithms based on exact difference schemes for nonlinear BVPs on the half-axis

    Article • Applied Numerical Mathematics, July 2009, Elsevier

    Volodymyr Makarov

  47. Generalized three-point difference schemes of high-order accuracy for systems of second-order nonlinear ordinary differential equations

    Article • Differential Equations, July 2009, Pleiades Publishing Ltd

    Volodymyr Makarov

  48. A Metod with a Controllable Exponential Convergence Rate for Nonlinear Differential Operator Equations

    Article • Computational Methods in Applied Mathematics, January 2009, De Gruyter

    Volodymyr Makarov

  49. Ivan Gavrilyuk — 60

    Article • Computational Methods in Applied Mathematics, January 2008, De Gruyter

    Volodymyr Makarov

  50. Two-Sided Approximations For Nonlinear Operator Equations

    Article • Computational Methods in Applied Mathematics, January 2008, De Gruyter

    Volodymyr Makarov

  51. Exponentially Convergent Duhamel-Like Algorithms for Differential Equations with an Operator Coefficient Possessing a Variable Domain in a Banach Space

    Article • SIAM Journal on Numerical Analysis, January 2008, Society for Industrial & Applied Mathematics (SIAM)

    Volodymyr Makarov

  52. An exponentially convergent algorithm for nonlinear differential equations in Banach spaces

    Article • Mathematics of Computation, October 2007, American Mathematical Society (AMS)

    Volodymyr Makarov

  53. Application of the FD-method to the solution of the Sturm-Liouville problem with coefficients of special form

    Article • Ukrainian Mathematical Journal, August 2007, Springer Science + Business Media

    Volodymyr Makarov

  54. Exponentially convergent parallel algorithm for nonlinear eigenvalue problems

    Article • IMA Journal of Numerical Analysis, April 2007, Oxford University Press (OUP)

    Volodymyr Makarov

  55. Difference Schemes for Nonlinear BVPS on the Semiaxis

    Article • Computational Methods in Applied Mathematics, January 2007, De Gruyter

    Volodymyr Makarov

  56. FD-method for a nonlinear eigenvalue problem with discontinuous eigenfunctions

    Article • Neliniini Kolyvannya, January 2007, Springer Science + Business Media

    Volodymyr Makarov

  57. FD-method for an eigenvalue problem with nonlinear potential

    Article • Ukrainian Mathematical Journal, January 2007, Springer Science + Business Media

    Volodymyr Makarov

  58. Mechanical systems, equivalent in Lyapunov's sense to systems not containing non-conservative positional forces

    Article • Journal of Applied Mathematics and Mechanics, January 2007, Elsevier

    Volodymyr Makarov

  59. Difference schemes for nonlinear BVPs using Runge-Kutta IVP-solvers

    Article • Advances in Difference Equations, January 2006, Springer Science + Business Media

    Volodymyr Makarov

  60. Exponentially Convergent Approximation to the Elliptic Solution Operator

    Article • Computational Methods in Applied Mathematics, January 2006, De Gruyter

    Volodymyr Makarov

  61. Taking into Account the Third Kind Conditions in Weight Estimates for Difference Schemes

    Article • January 2006, Springer Science + Business Media

    Volodymyr Makarov

  62. Exponentially Convergent Algorithms for the Operator Exponential with Applications to Inhomogeneous Problems in Banach Spaces

    Article • SIAM Journal on Numerical Analysis, January 2005, Society for Industrial & Applied Mathematics (SIAM)

    Volodymyr Makarov

  63. Functional-discrete Method (FD-method) for Matrix Sturm-Liouville Problems

    Article • Computational Methods in Applied Mathematics, January 2005, De Gruyter

    Volodymyr Makarov

  64. Functional-discrete Method for Eigenvalue Transmission Problem with Periodic Boundary Conditions

    Article • Computational Methods in Applied Mathematics, January 2005, De Gruyter

    Volodymyr Makarov

  65. Accuracy Estimates of Difference Schemes for Quasi-Linear Elliptic Equations with Variable Coefficients Taking into Account Boundary Effect

    Article • January 2005, Springer Science + Business Media

    Volodymyr Makarov

  66. Algorithms without accuracy saturation for evolution equations in Hilbert and Banach spaces

    Article • Mathematics of Computation, October 2004, American Mathematical Society (AMS)

    Volodymyr Makarov

  67. A Two-Sided Functional-Discrete Method for Second-Order Differential Equations with General Boundary Conditions

    Article • Differential Equations, July 2004, Springer Science + Business Media

    Volodymyr Makarov

  68. A New Estimate of the Sing Method for Linear Parabolic Problems Including the Initial Point

    Article • Computational Methods in Applied Mathematics, January 2004, De Gruyter

    Volodymyr Makarov

  69. A Two Point Difference Scheme of an Arbitrary Order of Accuracy for BVPS for Systems of First Order Nonlinear Odes

    Article • Computational Methods in Applied Mathematics, January 2004, De Gruyter

    Volodymyr Makarov

  70. Functional-Discrete Method with a High Order of Accuracy for the Eigenvalue Transmission Problem

    Article • Computational Methods in Applied Mathematics, January 2004, De Gruyter

    Volodymyr Makarov

  71. The stability of non-conservative systems with singular matrices of dissipative forces

    Article • Journal of Applied Mathematics and Mechanics, January 2004, Elsevier

    Volodymyr Makarov

  72. Nonclassical Asymptotic Formulas and Approximation with an Arbitrary Order of Accuracy of Eigenvalues of the Sturm-Liouville Problem with Bitsadze-Samarskii Conditions

    Article • Cybernetics and Systems Analysis, November 2003, Springer Science + Business Media

    Volodymyr Makarov

  73. A Parallel High-accuracy Method for the First-order Evolution Equation in Hilbert and Banach Spaces

    Article • Computational Methods in Applied Mathematics, January 2003, De Gruyter

    Volodymyr Makarov

  74. Accuracy Estimates of Difference Schemes for Quasi-linear Parabolic Equations Taking into Account the Initial-boundary Effect

    Article • Computational Methods in Applied Mathematics, January 2003, De Gruyter

    Volodymyr Makarov

  75. Raytcho Lazarov - 60

    Article • Computational Methods in Applied Mathematics, January 2003, De Gruyter

    Volodymyr Makarov

  76. The Two-sided FD-method of Solving the First Boundary Problem for Singular ODE of the Second Order in the Half-axis

    Article • Computational Methods in Applied Mathematics, January 2002, De Gruyter

    Volodymyr Makarov

  77. Stability and Regularization of Three-Level Difference Schemes with Unbounded Operator Coefficients in Banach Spaces

    Article • SIAM Journal on Numerical Analysis, January 2001, Society for Industrial & Applied Mathematics (SIAM)

    Volodymyr Makarov

  78. Exponentially Convergent Parallel Discretization Methods for the First Order Evolution Equations

    Article • Computational Methods in Applied Mathematics, January 2001, De Gruyter

    Volodymyr Makarov

  79. Integral Equations of the Linear Sloshing in an Infinite Chute and Their Discretization

    Article • Computational Methods in Applied Mathematics, January 2001, De Gruyter

    Volodymyr Makarov

  80. The theory of gyroscopic systems with non-conservative forces

    Article • Journal of Applied Mathematics and Mechanics, January 2001, Elsevier

    Volodymyr Makarov

  81. An Explicit Boundary Integral Representation of the Solution of the Two-Dimensional Heat Equation and Its Discretization

    Article • Journal of Integral Equations and Applications, March 2000, Rocky Mountain Mathematics Consortium

    Volodymyr Makarov

  82. On the Numerical Solution of Linear Evolution Problems with an Integral Operator Coefficient

    Article • Journal of Integral Equations and Applications, March 1999, Rocky Mountain Mathematics Consortium

    Volodymyr Makarov

  83. The Cayley transform and boundary integral equations to an initial boundary value problem for the heat equation

    Article • January 1999, Institute of Electrical & Electronics Engineers (IEEE)

    Volodymyr Makarov

  84. A fast algorithm for solving the dirichlet problem on hexagonal templet for the poisson equation in a rectangle

    Article • Journal of Mathematical Sciences, December 1995, Springer Science + Business Media

    Volodymyr Makarov

  85. The FD method for first-order linear hyperbolic differential equations with piecewise smooth coefficients

    Article • Journal of Mathematical Sciences, December 1995, Springer Science + Business Media

    Volodymyr Makarov

  86. Rate of convergence of the method of lines for the nonlinear parabolic integrodifferential equation describing a photon recycling diode

    Article • Journal of Mathematical Sciences, November 1994, Springer Science + Business Media

    Volodymyr Makarov

  87. Rate-of-convergence bounds of a finite-difference approximation of the Dirichlet problem for the Helmholtz equation with a coefficient from the “negative” space

    Article • Journal of Mathematical Sciences, September 1994, Springer Science + Business Media

    Volodymyr Makarov

  88. Solution of a singularly perturbed nonstationary fourth-order boundary-value problem

    Article • Journal of Mathematical Sciences, June 1994, Springer Science + Business Media

    Volodymyr Makarov

  89. Some issues of nonlinear functional system identification

    Article • Journal of Mathematical Sciences, May 1994, Springer Science + Business Media

    Volodymyr Makarov

  90. A line-method scheme for the quasi-inversion problem

    Article • Journal of Mathematical Sciences, March 1994, Springer Science + Business Media

    Volodymyr Makarov

  91. Rate of convergence bound of difference schemes for the first boundary-value problem of elasticity theory in arbitrary domains

    Article • Journal of Soviet Mathematics, September 1993, Springer Science + Business Media

    Volodymyr Makarov

  92. Rate-of-convergence bounds of the grid method for the axisymmetric Dirichlet problem in spherical geometry

    Article • Journal of Soviet Mathematics, August 1993, Springer Science + Business Media

    Volodymyr Makarov

  93. Solution of integral equations in fractional Sobolev spaces

    Article • Journal of Soviet Mathematics, August 1993, Springer Science + Business Media

    Volodymyr Makarov

  94. Accuracy bound of the grid method in optimal control problem for elliptic systems

    Article • Journal of Soviet Mathematics, February 1993, Springer Science + Business Media

    Volodymyr Makarov

  95. Rate-of-convergence bound for difference schemes for the system of equilibrium equations of a rigidly clamped nonhomogeneous anisotropic elastic solid

    Article • Journal of Soviet Mathematics, February 1993, Springer Science + Business Media

    Volodymyr Makarov

  96. A rate of convergence bound of regular-grid difference schemes for elliptical equations with discontinuous coefficients

    Article • Journal of Soviet Mathematics, January 1992, Springer Science + Business Media

    Volodymyr Makarov

  97. General structure of interpolational functional polynomials

    Article • Ukrainian Mathematical Journal, October 1991, Springer Science + Business Media

    Volodymyr Makarov

  98. Difference schemes for the dirichlet problem for an elliptical equation with discontinuous coefficients in an arbitrary region on a regular grid

    Article • Journal of Soviet Mathematics, April 1991, Springer Science + Business Media

    Volodymyr Makarov

  99. HOMOGENEOUS DIFFERENCE SCHEMES FOR ONE-DIMENSIONAL PROBLEMS WITH GENERALIZED SOLUTIONS

    Article • Mathematics of the USSR-Sbornik, February 1988, Turpion-Moscow Limited

    Volodymyr Makarov

  100. Matched convergence-rate estimates of the mesh method for the axisymmetric Poisson equation in spherical coordinates

    Article • USSR Computational Mathematics and Mathematical Physics, January 1987, Elsevier

    Volodymyr Makarov

  101. Matched estimates of the rate of convergence of the net method for Poisson's equation in polar coordinates

    Article • USSR Computational Mathematics and Mathematical Physics, January 1987, Elsevier

    Volodymyr Makarov

  102. Estimate of the convergence of the method of straight lines for equations of parabolic type

    Article • Ukrainian Mathematical Journal, January 1986, Springer Science + Business Media

    Volodymyr Makarov

  103. The rate of convergence of a difference scheme using the sun approximation method for generalized solutions

    Article • USSR Computational Mathematics and Mathematical Physics, January 1986, Elsevier

    Volodymyr Makarov

  104. Estimation of the rate of convergence of difference schemes for quasilinear elliptic equations of the fourth order

    Article • USSR Computational Mathematics and Mathematical Physics, January 1985, Elsevier

    Volodymyr Makarov

  105. Straight-line method for a quasilinear equation of parabolic type with nonclassical boundary condition

    Article • Ukrainian Mathematical Journal, January 1985, Springer Science + Business Media

    Volodymyr Makarov

  106. The convergence of difference solutions to the generalized solutions of the dirichlet problem for the helmholtz equation in a convex polygon

    Article • USSR Computational Mathematics and Mathematical Physics, January 1985, Elsevier

    Volodymyr Makarov

  107. Economic equilibrium: Existence and extremal property

    Article • Journal of Soviet Mathematics, August 1984, Springer Science + Business Media

    Volodymyr Makarov

  108. On the convergence of difference schemes for the approximation of solutionsu ? W 2 m (m>0.5) of elliptic equations with mixed derivatives

    Article • Numerische Mathematik, June 1984, Springer Science + Business Media

    Volodymyr Makarov

  109. APPLICATION OF EXACT DIFFERENCE SCHEMES TO THE CONSTRUCTION AND STUDY OF DIFFERENCE SCHEMES FOR GENERALIZED SOLUTIONS

    Article • Mathematics of the USSR-Sbornik, April 1983, Turpion-Moscow Limited

    Volodymyr Makarov

  110. Convergence of the interpolation process for an x2-analytic function

    Article • Ukrainian Mathematical Journal, January 1983, Springer Science + Business Media

    Volodymyr Makarov

  111. Leonid Vital'evich Kantorovich (on his seventieth birthday)

    Article • Russian Mathematical Surveys, June 1982, Turpion-Moscow Limited

    Volodymyr Makarov

  112. An algorithm for constructing completely conservative difference schemes

    Article • USSR Computational Mathematics and Mathematical Physics, January 1982, Elsevier

    Volodymyr Makarov

  113. Fast direct method for solving systems of linear algebraic equations with a block triangular matrix of a variable structure

    Article • Cybernetics, January 1982, Springer Science + Business Media

    Volodymyr Makarov

  114. Verification of circuit models for sampled-data radio-engineering systems

    Article • Cybernetics, January 1982, Springer Science + Business Media

    Volodymyr Makarov

  115. Difference scheme of second order of accuracy for the axisymmetric poisson equation in generalized solutions

    Article • USSR Computational Mathematics and Mathematical Physics, January 1981, Elsevier

    Volodymyr Makarov

  116. Algorithmic aspects of the method of summary representations

    Article • Ukrainian Mathematical Journal, January 1981, Springer Science + Business Media

    Volodymyr Makarov

  117. Use of exact difference schemes for estimating the rate of convergence of the method of straight lines

    Article • USSR Computational Mathematics and Mathematical Physics, January 1980, Elsevier

    Volodymyr Makarov

  118. Interpolation of hermite type in a class of x?-harmonic functions of given smoothness

    Article • Ukrainian Mathematical Journal, January 1980, Springer Science + Business Media

    Volodymyr Makarov

  119. A completely conservative difference scheme for gas-dynamic equations in Eulerian variables

    Article • USSR Computational Mathematics and Mathematical Physics, January 1980, Elsevier

    Volodymyr Makarov

  120. Two approaches to a numerical solution of a problem concerning impact on the surface of a solid elastic cylinder

    Article • Soviet Applied Mechanics, March 1979, Springer Science + Business Media

    Volodymyr Makarov

  121. Existence of economic equilibrium under conditions of multiplicity of forms of money and prices

    Article • Siberian Mathematical Journal, January 1979, Springer Science + Business Media

    Volodymyr Makarov

  122. Bounds on the zeros of a certain determinant whose elements are Bessel functions of the first and second kinds

    Article • Ukrainian Mathematical Journal, January 1973, Springer Science + Business Media

    Volodymyr Makarov

  123. Superlinear point-set maps and models of economic dynamics

    Article • Russian Mathematical Surveys, October 1970, Turpion-Moscow Limited

    Volodymyr Makarov

  124. Asymptotic behavior of optimum trajectories of linear economic models

    Article • Siberian Mathematical Journal, January 1967, Springer Science + Business Media

    Volodymyr Makarov