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Daghestan Electronic Mathematical Reports, 2017, Issue 8, Pages 100–109
(Mi demr88)
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This article is cited in 2 scientific papers (total in 2 papers)
An algorithm for the approximate solution of the Cauchy problem for systems of nonlinear ODEs using polynomials orthogonal in the Sobolev sense and generated by Chebyshev polynomials
M. S. Sultanakhmedov, T. I. Sharapudinov Daghestan Scientific Centre of Russian Academy of Sciences, Makhachkala
Abstract:
In current paper we propose an iterative method for solving the Cauchy problem for systems of nonlinear differential equations, which is based on the use of a system of functions orthogonal in the Sobolev sense and generated by the classical Chebyshev polynomials of the first kind $T_{n}(x) = \cos {(n \arccos{x})}$. The results of numerical experiments are presented.
Keywords:
Cauchy problem; Chebyshev polynomials of first kind; \linebreak numerical method; Sobolev inner product; system of differential equations.
Received: 14.11.2017 Revised: 21.12.2017 Accepted: 22.12.2017
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Abstract page: | 30 | References: | 6 |
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