Justification of an Approach to Application of Orthogonal Expansions for Approximate Integration of Canonical Systems of Second Order Ordinary Differential Equations / O. B. Arushanyan and S. F. Zaletkin. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2018. № 3. P. 29-33 [Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 111-115].

A solvability theorem for a nonlinear system of equations with respect to approximate values of Fourier–Chebyshev coefficients is proved. This theorem is a theoretical substantiation for the numerical solution of second order ordinary differential equations using Chebyshev series and Markov quadrature formulas.

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