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

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.