On the computation of approximate solution to ordinary differential equations by the Chebyshev series method and estimation of its errorстатья
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Дата последнего поиска статьи во внешних источниках: 9 апреля 2021 г.
Аннотация:Abstract—An approximate method for 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 anapproximate 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 for partitioning the integration interval into elementary subintervals to ensure the computation of the solution with a prescribed accuracy is constructed on the basis of the proposed approaches to error estimation.