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The use of Chebyshev series for approximate analytic solution of ordinary differential equations

O. B. Arushanyan, S. F. Zaletkin

Lomonosov Moscow State University, Research Computing Center

Abstract: Application of Chebyshev series to solve ordinary differential equations is described. This approach is based on the approximation of the solution to a given Cauchy problem and its derivatives by partial sums of shifted Chebyshev series. The coefficients of the series are determined by an iterative process using Markov quadrature formulas. It is shown that the proposed approach can be applied to formulate an approximate analytical method for solving Cauchy problems. A number of examples are considered to illustrate the obtaining of approximate analytical solutions in the form of partial sums of shifted Chebyshev series.

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

UDC: 519.622

Received: 14.03.2016

 English version: Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 2016, 71:5, 212–215

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