This article is cited in 12 papers

Mathematics

Calculation of expansion coefficients of series in Chebyshev polynomials for a solution to a Cauchy problem

O. B. Arushanyan, N. I. Volchenskova, S. F. Zaletkin

Lomonosov Moscow State University, Research Computing Center

Abstract: Two approaches are proposed to determine an initial approximation for the coefficients of an expansion of the solution to a Cauchy problem for ordinary differential equations in the form of series in shifted Chebyshev polynomials of the first kind. This approximation is used in an analytical method to solve ordinary differential equations using orthogonal expansions.

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

UDC: 519.622

Received: 08.11.2011

 English version: Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 2012, 67:5-6, 211–216

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