Об оценке погрешности приближенного решения обыкновенных дифференциальных уравнений, определенного с помощью рядов Чебышёва

О.Б. Арушанян, С.Ф. Залеткин
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
more » ... 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.
doi:10.26089/nummet.v21r321 fatcat:iy3elcrqafcxzplhimf7uxoyrq