DOI: https://doi.org/10.26089/NumMet.v17r212

Approximate solution of the Cauchy problem for ordinary differential equations by the method of Chebyshev series

Authors

  • O.B. Arushanyan
  • S.F. Zaletkin

Keywords:

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

Abstract

An approximate analytical method of solving the systems of ordinary differential equations resolved with respect to the derivatives of unknown functions is considered. This method is based on the approximation of the solution to the Cauchy problem and its derivatives by partial sums of shifted Chebyshev series. The coefficients of the series are determined by an iterative process with the use of Markov’s quadrature formulas. This approach can be used to solve ordinary differential equations with a higher accuracy and with a larger discretization step compared to the known Runge-Kutta and Adams methods.

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Published

2016-04-01

Issue

Vol. 17 (2016): Issue 2.

Section

Section 1. Numerical methods and applications

Author Biographies

O.B. Arushanyan

Lomonosov Moscow State University,
Research Computing Center
• Head of Laboratory

S.F. Zaletkin

Lomonosov Moscow State University,
Research Computing Center
• Senior Researcher

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