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Application of Chebyshev series to integration of ordinary differential equations with rapidly growing solutions

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

Lomonosov Moscow State University, Research Computing Center

Abstract: A method of solving systems of ordinary differential equations is described. This method is based on the approximation of right-hand sides by partial sums of shifted Chebyshev series. The coefficients of the series are determined using Markov quadrature formulas. It is shown that the proposed method is more efficient compared to the Runge–Kutta and Adams methods when solving differential equations with rapidly growing solutions.

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

UDC: 519.622

Received: 24.09.2014

 English version: Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 2015, 70:5, 237–240

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