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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2014, Volume 54, Number 1, Pages 13–24
DOI: https://doi.org/10.7868/S0044466914010062
(Mi zvmmf9970)
 

This article is cited in 26 scientific papers (total in 26 papers)

Method of fast expansions for solving nonlinear differential equations

A. D. Chernyshov

Voronezh State University of Engineering Technologies, pr. Revolyutsii 19, Voronezh, 394000, Russia
References:
Abstract: A method is proposed for constructing fast converging Fourier series with the help of a special boundary function $M_q$. The convergence rate of the series is determined by the order $q$ of $M_q$, which makes it possible to use a small number of series terms. The general theory of constructing fast expansions is described, the error of the partial sum of a series is estimated, and an example of a non-linear integrodifferential problem is considered. Due to its remarkable properties, the fast expansion method can be effectively used in applications.
Key words: fast expansions, Fourier series, error estimate, uniform convergence, nonlinear integrodifferential equations.
Received: 19.11.2010
Revised: 22.04.2012
English version:
Computational Mathematics and Mathematical Physics, 2014, Volume 54, Issue 1, Pages 11–21
DOI: https://doi.org/10.1134/S0965542514010060
Bibliographic databases:
Document Type: Article
UDC: 519.651
Language: Russian
Citation: A. D. Chernyshov, “Method of fast expansions for solving nonlinear differential equations”, Zh. Vychisl. Mat. Mat. Fiz., 54:1 (2014), 13–24; Comput. Math. Math. Phys., 54:1 (2014), 11–21
Citation in format AMSBIB
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  • This publication is cited in the following 26 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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    References:103
    First page:21
     
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