Solvability of a System of Equations for the Fourier–Chebyshev Coefficients when Solving Ordinary Differential Equations by the Chebyshev Series Method / O. B. Arushanyan and S. F. Zaletkin. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2017. № 5. P. 58-61 [Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 213-216].

A solvability theorem for a system of equations with respect to approximate values of Fourier–Chebyshev coefficients is formulated. This theorem is a theoretical justification for numerical solution of ordinary differential equations using Chebyshev series.

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