On an approximate analytical method of solving ordinary differential equations

Authors

  • O.B. Arushanyan Lomonosov Moscow State University
  • N.I. Volchenskova Lomonosov Moscow State University
  • S.F. Zaletkin Lomonosov Moscow State University

DOI:

https://doi.org/10.26089/NumMet.v16r223

Keywords:

ordinary differential equations, approximate analytical methods, numerical methods, orthogonal expansions, shifted Chebyshev series, Markov’s quadrature formulas

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.

Author Biographies

O.B. Arushanyan

N.I. Volchenskova

S.F. Zaletkin

References

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  12. O. B. Arushanyan, N. I. Volchenskova, and S. F. Zaletkin, “Calculation of the Coefficients of Orthogonal Expansions for the Solutions to Ordinary Differential Equations,” Differen. Uravn. Protsessy Upravl. 15 (2), 41-47 (2011).
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  17. O. B. Arushanyan, N. I. Volchenskova, and S. F. Zaletkin, “On an Approach to Integration of Ordinary Differential Equations with the Use of Series,” Vestn. Mosk. Univ., Ser. 1: Mat. Mekh., No. 6, 57-60 (2014) [Moscow Univ. Math. Bull. 69 (6), 272-274 (2014)].

Published

06-05-2015

How to Cite

Арушанян О.Б., Волченскова Н.И., Залеткин С.Ф. On an Approximate Analytical Method of Solving Ordinary Differential Equations // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2015. 16. 235-241. doi 10.26089/NumMet.v16r223

Issue

Section

Section 1. Numerical methods and applications

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