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
A method of using Markov's quadrature with one and two fixed nodes is proposed to calculate the coefficients of the expansion of a function in a Chebyshev shifted series. Approximation properties of a partial sum of the series with approximate coefficients are considered. This approach can be used to construct a number of numerical analytic methods for solving ordinary differential equations.