"To the orthogonal expansion theory of the solution to the Cauchy problem for second-order ordinary differential equations"
Arushanyan O.B. and Zaletkin S.F.

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.

  • Arushanyan O.B. – Research Computing Center, Lomonosov Moscow State University; Leninskie Gory, Moscow, 119992, Russia; Dr. Sci., Professor, Head of Laboratory, e-mail: arush@srcc.msu.ru
  • Zaletkin S.F. – Research Computing Center, Lomonosov Moscow State University; Leninskie Gory, Moscow, 119992, Russia; Ph.D., Senior Scientist, e-mail: iraz@srcc.msu.ru