### Approximation theory

### Daghestan Electronic Mathematical Reports: Issue 8 (2017)

# 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

### UDK: 519.622

### Pages: 53 - 60

### 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.