Geodesic
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.

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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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     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},
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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/

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