On an approximate method of integration of ordinary differential equations / *O. B. Arushanyan, N. Volchenskova, S. nd Zaletkin.* // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2013. № 6. P. 43-46
[Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 0].

An approximate analytical method of solving a Cauchy problem for normal systems of ordinary differential equations is considered. The method is based on the approximation of the solution by partial sums of shifted Chebyshev series. The coefficients of the series are determined by an iterative process using Markov quadrature formulas.

*Key words*:
ordinary differential equations, approximate analytical methods, numerical methods, orthogonal expansions, shifted Chebyshev polynomials, Markov quadrature formulas.