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 
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/
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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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     year = {2020},
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     url = {http://geodesic.mathdoc.fr/item/VMUMM_2020_5_a2/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Arushanyan O.B., Zaletkin S.F., “Priblizhennoe reshenie zadachi Koshi dlya obyknovennykh differentsialnykh uravnenii metodom ryadov Chebysheva”, Vychisl. metody i program., 17 (2016), 121–131

[2] Arushanyan O.B., Volchenskova N.I., Zaletkin S.F., “Vychislenie koeffitsientov razlozheniya resheniya zadachi Koshi v ryad po mnogochlenam Chebysheva”, Vestn. Mosk. un-ta. Matem. Mekhan., 2012, no. 5, 24–30

[3] Arushanyan O.B., Zaletkin S.F., “Ispolzovanie ryadov Chebysheva dlya priblizhennogo analiticheskogo resheniya obyknovennykh differentsialnykh uravnenii”, Vestn. Mosk. un-ta. Matem. Mekhan., 2016, no. 5, 52–56

[4] Arushanyan O.B., Zaletkin S.F., “O razreshimosti sistemy uravnenii otnositelno koeffitsientov Fure–Chebysheva pri reshenii obyknovennykh differentsialnykh uravnenii metodom ryadov Chebysheva”, Vestn. Mosk. un-ta. Matem. Mekhan., 2017, no. 5, 58–61

[5] Arushanyan O.B., Zaletkin S.F., “O primenenii formuly chislennogo integrirovaniya Markova v ortogonalnykh razlozheniyakh”, Vestn. Mosk. un-ta. Matem. Mekhan., 2009, no. 6, 18–22