This article is cited in 10 papers

On calculation of Chebyshev series coefficients for the solutions to ordinary differential equations

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

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

Abstract: Canonical systems of second-order ordinary differential equations are considered. The solution of such a system and its derivatives are expanded in shifted series in Chebyshev polynomials of the first kind. Algorithms to determine initial approximations for the expansion coefficients are described. The resulting approximations are used in the method of approximate analytical integration of ordinary differential equations on the basis of Chebyshev series.

Keywords: ordinary differential equations, numerical methods.

UDC: 519.62

MSC: 65L05

Received April 26, 2011, published September 14, 2011