"On solvability of a nonlinear system of equations for the Fourier-Chebyshev coefficients in the problem of solving ordinary differential equations using Chebyshev series"
Arushanyan O.B. and Zaletkin S.F.

A solvability theorem for a nonlinear system of equations with respect to approximate values of Fourier-Chebyshev coefficients is formulated and proved. This theorem is a theoretical substantiation for the previously proposed numerical-analytical method of solving ordinary differential equations using Chebyshev series.

Keywords: ordinary differential equations, 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