Geodesic
Approximate integration of the canonical systems of second order ordinary differential equations with the use of Chebyshev series with error estimation for solution and its derivative
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2022), pp. 27-34 
O. B. Arushanyan; S. F. Zaletkin. Approximate integration of the canonical systems of second order ordinary differential equations with the use of Chebyshev series with error estimation for solution and its derivative. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2022), pp. 27-34. http://geodesic.mathdoc.fr/item/VMUMM_2022_4_a3/
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     author = {O. B. Arushanyan and S. F. Zaletkin},
     title = {Approximate integration of the canonical systems of second order ordinary differential equations with the use of {Chebyshev} series with error estimation for solution and its derivative},
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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 canonical second-order ordinary differential equations is considered. This method is based on using the shifted Chebyshev series and a Markov quadrature formula. A number of procedures are discussed to estimate the error of the approximate solution and its derivative expressed by partial sums of shifted Chebyshev series of a certain order. The error is estimated using the second approximate solution obtained by a special way and represented by a partial sum of higher order. The proposed procedures are used to develop an algorithm to partition the integration interval into elementary subintervals, which allows one to compute an approximate solution and its derivative with a prescribed accuracy.

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[2] Arushanyan O. B., Volchenskova N. I., Zaletkin S. F., “O primenenii ortogonalnykh razlozhenii dlya priblizhennogo integrirovaniya obyknovennykh differentsialnykh uravnenii”, Vestn. Mosk. un-ta. Matem. Mekhan., 2010, no. 4, 40–43 | MR | Zbl

[3] 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 | Zbl

[4] Arushanyan O. B., Zaletkin S. F., “Obosnovanie odnogo podkhoda k primeneniyu ortogonalnykh razlozhenii dlya priblizhennogo integrirovaniya kanonicheskikh sistem obyknovennykh differentsialnykh uravnenii vtorogo poryadka”, Vestn. Mosk. un-ta. Matem. Mekhan., 2018, no. 3, 29–33 | MR | Zbl

[5] Arushanyan O. B., Zaletkin S. F., “Ob odnom analiticheskom metode priblizhennogo resheniya kanonicheskikh sistem obyknovennykh differentsialnykh uravnenii vtorogo poryadka”, Vestn. Mosk. un-ta. Matem. Mekhan., 2019, no. 3, 65–69 | Zbl

[6] 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 | Zbl

[7] Zaletkin S. F., “Formula chislennogo integrirovaniya Markova s dvumya fiksirovannymi uzlami i ee primenenie v ortogonalnykh razlozheniyakh”, Vychislitelnye metody i programmirovanie, 6:3 (2005), 1–17

[8] Arushanyan O. B., Zaletkin S. F., “O vychislenii priblizhennogo resheniya obyknovennykh differentsialnykh uravnenii metodom ryadov Chebysheva i otsenka ego pogreshnosti”, Vestn. Mosk. un-ta. Matem. Mekhan., 2020, no. 5, 22–26 | Zbl