O. B. Arushanyan
Research Computing Center
Moscow State University
Leninskie Gori, Moscow
119991, Russia
N. I. Volchenskova
Research Computing Center
Moscow State University
Leninskie Gori, Moscow
119991, Russia
S. F. Zaletkin
Research Computing Center
Moscow State University
Leninskie Gori, Moscow
119991, Russia
An approximate method of solving the Cauchy problem for normal and canonical systems of ordinary differential equations is proposed. The method is based on orthogonal expansions of the solution and its derivative in shifted series of Chebyshev polynomials. The corresponding equations are constructed for the approximate values of Chebyshev coefficients in the right-hand side of the system under study. An iterative process for solving these equations is described and the sufficient conditions of its convergence are considered. Some asymptotic error estimates in the approximate Chebyshev coefficients and in the solution are given with respect to the size of the integration step.