This article is cited in 3 papers

Mathematics

Justification of some approach to implementation of orthogonal expansions for approximate integration of canonical systems of second order ordinary differential equations

O. B. Arushanyan, S. F. Zaletkin

Lomonosov Moscow State University, Research Computing Center

Abstract: A solvability theorem for a nonlinear system of equations with respect to approximate values of Fourier–Chebyshev coefficients is proved. This theorem is a theoretical substantiation for the numerical solution of second order ordinary differential equations using Chebyshev series and Markov quadrature formulas.

Key words: ordinary differential equations, approximate analytical methods, numerical methods, orthogonal expansions, shifted Chebyshev series, Markov quadrature formulas.

UDC: 519.622

Received: 19.12.2017

 English version: Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 2018, 73:3, 111–115

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