To the orthogonal expansion theory of the solution to the Cauchy problem for second-order ordinary differential equations
DOI:
https://doi.org/10.26089/NumMet.v19r216Keywords:
ordinary differential equations, Cauchy problem, approximate analytical methods, numerical methods, orthogonal expansions, shifted Chebyshev series, Markov’s quadrature formulasAbstract
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.
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