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 Num. Meth. Prog., 2015, Volume 16, Issue 2, Pages 235–241 (Mi vmp535)

On an approximate analytical method of solving ordinary differential equations

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

Lomonosov Moscow State University, Research Computing Center

Abstract: The application of shifted Chebyshev series for solving ordinary differential equations is described. This approach is based on the approximation of the solution to the Cauchy problem for a normal system of ordinary differential equations and its derivatives by partial sums of Fourier series in the Chebyshev polynomials of the first kind. The coefficients of the series are determined by an iterative process with the use of Markov's quadrature formulas. The approximation properties of shifted Chebyshev series allow us to propose an approximate analytical method for ordinary differential equations. A number of examples are considered to illustrate the application of partial sums of Chebyshev series for approximate representations of the solutions to the Cauchy problems for ordinary differential equations.

Keywords: ordinary differential equations, approximate analytical methods, numerical methods, orthogonal expansions, shifted Chebyshev series, Markov's quadrature formulas.

Full text: PDF file (167 kB)
UDC: 519.62

Citation: O. B. Arushanyan, N. I. Volchenskova, S. F. Zaletkin, “On an approximate analytical method of solving ordinary differential equations”, Num. Meth. Prog., 16:2 (2015), 235–241

Citation in format AMSBIB
\Bibitem{AruVolZal15} \by O.~B.~Arushanyan, N.~I.~Volchenskova, S.~F.~Zaletkin \paper On an approximate analytical method of solving ordinary differential equations \jour Num. Meth. Prog. \yr 2015 \vol 16 \issue 2 \pages 235--241 \mathnet{http://mi.mathnet.ru/vmp535}