An algorithm for the approximate solution of the Cauchy problem for systems of nonlinear ODEs using polynomials orthogonal in the Sobolev sense and generated by Chebyshev polynomials

Pages: 100 - 109

In current paper we propose an iterative method for solving the Cauchy problem for systems of nonlinear differential equations, which is based on the use of a system of functions orthogonal in the Sobolev sense and generated by the classical Chebyshev polynomials of the first kind $T_{n}(x) = \cos {(n \arccos{x})}$. The results of numerical experiments are presented.

﻿