This article is cited in 4 papers

Approximate integration of ordinary differential equations using Chebyshev series with precision control

S. F. Zaletkin

Research Computing Center, Lomonosov Moscow State University

Abstract: An approximate method of solving the Cauchy problem for canonical systems of second order ordinary differential equations is considered. The method is based on using the shifted Chebyshev series and a Markov quadrature formula. Some approaches are given to estimate the errors of an approximate solution and its derivative expressed by partial sums of a certain order shifted Chebyshev series. The errors are estimated using the second approximation of the solution calculated in a special way and expressed by a partial sum of a higher order series. An algorithm of partitioning the integration interval into elementary subintervals to ensure the computation of the solution and its derivative with prescribed accuracy is discussed on the basis of proposed approaches to error estimation.

Keywords: ordinary differential equations, approximate analytical methods, numerical methods, orthogonal expansions, shifted Chebyshev series, Markov quadrature formulas, polynominal approximation, precision control, error estimate, automatic step size control.

Received: 11.01.2022
Revised: 28.02.2022
Accepted: 14.03.2022

DOI: 10.20948/mm-2022-06-04

 English version: Mathematical Models and Computer Simulations, 2023, 15:1, 34–46

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