A numerical method for solving the Cauchy problem for systems of ordinary differential equations by means of a system orthogonal in the sense of Sobolev generated by the cosine system

I. I. Sharapudinov; M. G. Magomed-Kasumov

Geodesic

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A numerical method for solving the Cauchy problem for systems of ordinary differential equations by means of a system orthogonal in the sense of Sobolev generated by the cosine system

I. I. Sharapudinov ; M. G. Magomed-Kasumov

Daghestan Electronic Mathematical Reports, Tome 8 (2017), pp. 53-60

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Résumé

We consider iterative method that numerically solves Cauchy problem for systems of equations. Suggested method is based on using sobolev orthogonal system of functions, generated by cosine system $\{1, \sqrt{2}\cos(\pi k x), \; k \ge 1 \}$.

Keywords: Cauchy problem, numerical method, Sobolev inner product, system of differential equations.

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     author = {I. I. Sharapudinov and M. G. Magomed-Kasumov},
     title = {A numerical method for solving the {Cauchy} problem for systems of ordinary differential equations by means of a system orthogonal in the sense of {Sobolev} generated by the cosine system},
     journal = {Daghestan Electronic Mathematical Reports},
     pages = {53--60},
     publisher = {mathdoc},
     volume = {8},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DEMR_2017_8_a5/}
}

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I. I. Sharapudinov; M. G. Magomed-Kasumov. A numerical method for solving the Cauchy problem for systems of ordinary differential equations by means of a system orthogonal in the sense of Sobolev generated by the cosine system. Daghestan Electronic Mathematical Reports, Tome 8 (2017), pp. 53-60. http://geodesic.mathdoc.fr/item/DEMR_2017_8_a5/