DOI: https://doi.org/10.26089/NumMet.v21r321

An error estimate for an approximate solution to ordinary differential equations obtained using the Chebyshev series

Authors

  • O.B. Arushanyan
  • S.F. Zaletkin

Keywords:

ordinary differential equations
approximate analytical methods
numerical methods
orthogonal expansions
shifted Chebyshev series
Markov quadrature formulas
polynomial approximation
precision control
error estimate
automatic step size control

Abstract

An approximate method of solving the Cauchy problem for nonlinear first-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 error of an approximate solution expressed by a partial sum of a certain order series. The error is estimated using the second approximation of the solution 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 with a prescribed accuracy is discussed on the basis of the proposed approaches to error estimation.

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Published

2020-09-27

Issue

Vol. 21 (2020): Issue 3.

Section

Methods and algorithms of computational mathematics and their 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

References

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