Mathematical Model of the Graded-Band-Gap Semiconductor Structure with High Internal Quantum Efficiency. - Ivan P. Gavrilyuk; Nataliya Rossokhataya; Victor Rossokhaty; Volodymyr L. Makarov (SIAM J. Appl. Math., 1999)

Stability and Regularization of Three-Level Difference Schemes with Unbounded Operator Coefficients in Banach Spaces. - Alexander Samarskii; Ivan P. Gavrilyuk; Volodymyr L. Makarov (SIAM J. Numer. Anal., 2001)

Accuracy Estimates of Difference Schemes for Quasi-Linear Elliptic Equations with Variable Coefficients Taking into Account Boundary Effect. - Volodymyr L. Makarov; Lyubomyr I. Demkiv (NAA, 2004)

Taking into Account the Third Kind Conditions in Weight Estimates for Difference Schemes. - Volodymyr L. Makarov; Lyubomyr I. Demkiv (LSSC, 2005)

Algorithms without accuracy saturation for evolution equations in Hilbert and Banach spaces. - Ivan P. Gavrilyuk; Volodymyr L. Makarov (Math. Comput., 2005)

Exponentially Convergent Algorithms for the Operator Exponential with Applications to Inhomogeneous Problems in Banach Spaces. - Ivan P. Gavrilyuk; Volodymyr L. Makarov (SIAM J. Numer. Anal., 2005)

An exponentially convergent algorithm for nonlinear differential equations in Banach spaces. - Ivan P. Gavrilyuk; Volodymyr L. Makarov (Math. Comput., 2007)

Exponentially Convergent Duhamel-Like Algorithms for Differential Equations with an Operator Coefficient Possessing a Variable Domain in a Banach Space. - T. Yu. Bohonova; Ivan P. Gavrilyuk; Volodymyr L. Makarov; Vitalii B. Vasylyk (SIAM J. Numer. Anal., 2007)

Weight Uniform Accuracy Estimates of Finite Difference Method for Poisson Equation, Taking into Account Boundary Effect. - Volodymyr L. Makarov; Lyubomyr I. Demkiv (NAA, 2008)

A Metod with a Controllable Exponential Convergence Rate for Nonlinear Differential Operator Equations. - Ivan P. Gavrilyuk; I. I. Lazurchak; Volodymyr L. Makarov; Dmytro Sytnyk (Comput. Methods Appl. Math., 2009)

Two-point difference schemes of an arbitrary given order of accuracy for nonlinear BVPs. - Ivan P. Gavrilyuk; Martin Hermann; Myroslav V. Kutniv; Volodymyr L. Makarov (Appl. Math. Lett., 2010)

A numerical-analytic method for solving the Cauchy problem for ordinary differential equations. - Volodymyr L. Makarov; Denys Dragunov (Comput. Methods Appl. Math., 2011)

Exponentially Convergent Functional-discrete Method for Eigenvalue Transmission Problems with a Discontinuous Flux and the Potential as a Function in the Space L_1. - Volodymyr L. Makarov; Nataliya Rossokhata; Denys Dragunov (Comput. Methods Appl. Math., 2012)

Stability and Regularization of Difference Schemes in Banach and Hilbert Spaces. - Ivan P. Gavrilyuk; Volodymyr L. Makarov (Comput. Methods Appl. Math., 2013)

An exponentially convergent functional-discrete method for solving Sturm-Liouville problems with a potential including the Dirac δ-function. - Volodymyr L. Makarov; Nataliya Rossokhata; Denys Dragunov (J. Comput. Appl. Math., 2013)

The FD-method for solving Sturm-Liouville problems with special singular differential operator. - Volodymyr L. Makarov; Denys Dragunov; Ya. V. Klimenko (Math. Comput., 2013)

On the interpolation of a function on a bounded domain by its traces on parametric hypersurfaces. - Roman Chapko; Christina Babenko; Volodymyr Khlobystov; Volodymyr L. Makarov (Int. J. Comput. Math., 2014)

Super-Exponentially Convergent Parallel Algorithm for Eigenvalue Problems with Fractional Derivatives. - Lyubomyr I. Demkiv; Ivan P. Gavrilyuk; Volodymyr L. Makarov (Comput. Methods Appl. Math., 2016)

Super-Exponentially Convergent Parallel Algorithm for a Fractional Eigenvalue Problem of Jacobi-Type. - Ivan P. Gavrilyuk; Volodymyr L. Makarov; Nataliia Romaniuk (Comput. Methods Appl. Math., 2018)

Symbolic Algorithm of the Functional-Discrete Method for a Sturm-Liouville Problem with a Polynomial Potential. - Volodymyr L. Makarov; Nataliia Romaniuk (Comput. Methods Appl. Math., 2018)

The Boundary Effect in the Accuracy Estimate for the Grid Solution of the Fractional Differential Equation. - Volodymyr L. Makarov; Nataliya V. Mayko (Comput. Methods Appl. Math., 2019)

An efficient approach for solving stiff nonlinear boundary value problems. - Volodymyr L. Makarov; Denys Dragunov (J. Comput. Appl. Math., 2019)

Exponentially convergent symbolic algorithm of the functional-discrete method for the fourth order Sturm-Liouville problems with polynomial coefficients. - Volodymyr L. Makarov; Nataliia Romaniuk (J. Comput. Appl. Math., 2019)

Weighted Estimates for Boundary Value Problems with Fractional Derivatives. - Ivan P. Gavrilyuk; Volodymyr L. Makarov; Nataliya V. Mayko (Comput. Methods Appl. Math., 2020)

Weighted estimates of the Cayley transform method for boundary value problems in a Banach space. - Volodymyr L. Makarov; Nataliya V. Mayko (CoRR, 2020)

Weighted Estimates of the Cayley Transform Method for Abstract Differential Equations. - Ivan P. Gavrilyuk; Volodymyr L. Makarov; Nataliya V. Mayko (Comput. Methods Appl. Math., 2021)

Numerical method for abstract Cauchy problem with nonlinear nonlocal condition. - Volodymyr L. Makarov; Dmytro Sytnyk; Vitalii B. Vasylyk (CoRR, 2024)

Exponentially convergent method for time-fractional evolution equation. - Vitalii B. Vasylyk; Volodymyr L. Makarov (CoRR, 2024)