O.B. Arushanyan, N.I. Volchenskova, and S.F. Zaletkin. Application of orthogonal expansions for approximate integration of ordinary differential equations // Moscow Univ. Math. Bull. 2010. Vol. 65, No. 4. 172-175.
A numerical analytical method is proposed to solve the Cauchy problem for systems of first-order ordinary differential equations. The method is based on the application of shifted Chebyshev polynomials of the first kind whose coefficients are calculated with the aid of Markov quadratures.
ordinary differential equations, Cauchy problem, Markov quadrature, Chebyshev polynomials