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.
References
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- O. B. Arushanyan, N. I. Volchenskova, and S. F. Zaletkin, “Calculation of Expansion Coefficients of Series in Chebyshev Polynomials for a Solution to a Cauchy Problem,” Vestn. Mosk. Univ., Ser. 1: Mat. Mekh., No. 5, 24-30 (2012) [Moscow Univ. Math. Bull. 67 (5-6), 211-216 (2012)].
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Published
02-05-2018
How to Cite
Арушанян О., Залеткин С. To the Orthogonal Expansion Theory of the Solution to the Cauchy Problem for Second-Order Ordinary Differential Equations // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2018. 19. 178-184. doi 10.26089/NumMet.v19r216
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Section
Section 1. Numerical methods and applications
