This article is cited in 7 papers

Research papers

Approximate solution of ordinary differential equations using Chebyshev series

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

Research Computer Center, M. V. Lomonosov Moscow State University

Abstract: An approximate method to solve the Cauchy problem for normal and canonical systems of second-order ordinary differential equations is proposed. The method is based on orthogonal expansions of the solution and its derivative in shifted series of Chebyshev polynomials of the first kind at the integration step. The corresponding equations are constructed for the approximate values of Chebyshev coefficients in the right-hand side of the system under study. An iterative process for solving these equations is described and some sufficient conditions of its convergence are considered. Several error estimates for the Chebyshev coefficients and for the solution are given with respect to the size of the integration step.

Keywords: ordinary differential equations, numerical methods.

UDC: 519.62

MSC: 65L05

Received December 20, 2009, published June 29, 2010

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