An error estimate for an approximate solution to ordinary differential equations obtained using the Chebyshev series
DOI:
https://doi.org/10.26089/NumMet.v21r321Keywords:
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 controlAbstract
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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