This article is cited in 4 papers

To the orthogonal expansion theory of the solution to the Cauchy problem for second-order ordinary differential equations

O. B. Arushanyan, S. F. Zaletkin

Lomonosov Moscow State University, Research Computing Center

Abstract: A solvability theorem is proved for a nonlinear system of equations with respect to the approximate Chebyshev coefficients of the highest derivative in an ordinary differential equation. This theorem is a theoretical substantiation for the previously proposed approximate method of solving canonical systems of second-order ordinary differential equations using orthogonal expansions on the basis of Chebyshev polynomials of the first kind.

Keywords: ordinary differential equations, Cauchy problem, approximate analytical methods, numerical methods, orthogonal expansions, shifted Chebyshev series, Markov's quadrature formulas.

UDC: 519.622

Received: 21.03.2018