M. G. Magomed-Kasumov, S. R. Magomedov, “The spectral method for solving the Cauchy problem for systems of ordinary differential equations by means of a system of functions orthogonal in the sense of Sobolev, generated by the Haar system”, Daghestan Electronic Mathematical Reports, 2018, Issue 10,Pages <nobr>50

The spectral method for solving the Cauchy problem for systems of ordinary differential equations by means of a system of functions orthogonal in the sense of Sobolev, generated by the Haar system

M. G. Magomed-Kasumov^ab, S. R. Magomedov^b

^a Vladikavkaz Scientific Centre of the Russian Academy of Sciences
^b Daghestan Scientific Centre of Russian Academy of Sciences, Makhachkala

Abstract: We consider an iterative method that numerically solves Cauchy problem for systems of equations. Suggested method is based on using Sobolev orthogonal system of functions, generated by Haar functions $\{1, \chi_n, 2^k < n \leq 2^{k+1}, k \geq 1\}$.

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

UDC: 519.622

Received: 14.11.2018
Revised: 10.12.2018
Accepted: 11.12.2018

DOI: 10.31029/demr.10.5