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An approximate method for integration of ordinary differential equations

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

Lomonosov Moscow State University, Research Computing Center

Abstract: An approximate analytical method of solving a Cauchy problem for normal systems of ordinary differential equations is considered. The method is based on the approximation of the solution by partial sums of shifted Chebyshev series. The coefficients of the series are determined by an iterative process using Markov quadrature formulas.

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

UDC: 519.622

Received: 10.02.2013

 English version: Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 2013, 68:6, 292–294

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