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
The solutions of ordinary differential equations and their derivatives are expanded in series in Chebyshev polynomials of the first kind. Two approaches are proposed to determine an initial approximation for the expansion coefficients. The resulting approximations are intended for use in the method of approximate analytical integration of ordinary differential equations on the basis of orthogonal expansions.