# 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

### DOI: 10.31029/demr.8.6

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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