Geodesic
Calculation of expansion coefficients of series in Chebyshev polynomials for a solution to a Cauchy problem
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2012), pp. 24-30 
O. B. Arushanyan; N. I. Volchenskova; S. F. Zaletkin. Calculation of expansion coefficients of series in Chebyshev polynomials for a solution to a Cauchy problem. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2012), pp. 24-30. http://geodesic.mathdoc.fr/item/VMUMM_2012_5_a4/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Two approaches are proposed to determine an initial approximation for the coefficients of an expansion of the solution to a Cauchy problem for ordinary differential equations in the form of series in shifted Chebyshev polynomials of the first kind. This approximation is used in an analytical method to solve ordinary differential equations using orthogonal expansions.

[1] 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

[2] Babenko K.I., Osnovy chislennogo analiza, Nauka, M., 1986 | MR

[3] Mysovskikh I.P., Lektsii po metodam vychislenii, Izd-vo SPb. un-ta, SPb., 1998 | MR

[4] Ilin V.P., Kuznetsov Yu.I., Algebraicheskie osnovy chislennogo analiza, Nauka, Novosibirsk, 1986 | MR

[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 | MR

[6] Zaletkin S.F., “Formula chislennogo integrirovaniya Markova s dvumya fiksirovannymi uzlami i ee primenenie v ortogonalnykh razlozheniyakh”, Vychislitelnye metody i programmirovanie, 6:1 (2005), 141–157

[7] Bakhvalov N.S., Zhidkov N.P., Kobelkov G.M., Chislennye metody, BINOM, M., 2007 | MR

[8] Arushanyan O.B., Zaletkin S.F., Chislennoe reshenie obyknovennykh differentsialnykh uravnenii na Fortrane, Izd-vo MGU, M., 1990 | MR

[9] Pashkovskii S., Vychislitelnye primeneniya mnogochlenov i ryadov Chebysheva, Nauka, M., 1983 | MR