Arushanyan O.B., Volchenskova N.I., Zaletkin S.F. Calculation of expansion coefficients of series in Chebyshev polynomials for a solution to a Cauchy problem // Moscow University Mathematics Bulletin.2012. Vol. 67, N 5/6. 211-216.
Canonical systems of first-order ordinary differential equations are considered. The solution of such a system and its derivatives are expanded in shifted series in Chebyshev polynomials of the first kind. Algorithms to determine the expansion coefficients are described. The resulting approximations are used in the method of approximate analytical integration of ordinary differential equations on the basis of Chebyshev series
ordinary differential equations, numerical methods