Geodesic
On the computation of approximate solution to ordinary differential equations by the Chebyshev series method and estimation of its error
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2020), pp. 22-26

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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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     author = {O. B. Arushanyan and S. F. Zaletkin},
     title = {On the computation of approximate solution to ordinary differential equations by the {Chebyshev} series method and estimation of its error},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
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O. B. Arushanyan; S. F. Zaletkin. On the computation of approximate solution to ordinary differential equations by the Chebyshev series method and estimation of its error. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2020), pp. 22-26. http://geodesic.mathdoc.fr/item/VMUMM_2020_5_a2/