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On some analytic method for approximate solution of systems of second order ordinary differential equations

O. B. Arushanyan, S. F. Zaletkin

Lomonosov Moscow State University, Research Computing Center

Abstract: An approach to using Chebyshev series to solve canonical second-order ordinary differential equations is described. This approach is based on the approximation of the solution to the Cauchy problem and its first and second derivatives by partial sums of shifted Chebyshev series. The coefficients of the series are determined by an iterative process using the Markov quadrature formula. It is shown that the described approach allows one to propose an approximate analytical method of solving the Cauchy problem. A number of canonical second-order ordinary differential equations are considered to represent their approximate analytical solutions in the form of partial sums of shifted Chebyshev series.

Key words: ordinary differential equations, canonical systems of second-order ordinary differential equations, approximate analytical methods, numerical methods, orthogonal expansions, shifted Chebyshev series, Markov quadrature formulas.

UDC: 519.622

Received: 15.11.2018

 English version: Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 2019, 74:3, 127–130

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