Approximate Integration of Ordinary Differential Equations Using the Chebyshev Series with Precision Controlстатья
Информация о цитировании статьи получена из
Scopus
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 1 мая 2024 г.
Аннотация:An approximate method of solving the Cauchy problem for canonical systems of second 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 errors of an approximate solution and its derivative expressed by partial sums of a certain order of shifted Chebyshev series. The errors are estimated using the second approximation of the solution calculated in a special way and 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 and its derivative with the prescribed accuracy is discussed based on the proposed approaches to estimating errors.