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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2010, Volume 13, Number 4, Pages 413–422 (Mi sjvm416)  
This article is cited in 1 scientific paper (total in 1 paper)

A step-by-step method with Laguerre functions for solving time-dependent problems

G. V. Demidov, V. N. Martynov

Institute of Computational Mathematics and Mathematical Geophysics (Computing Center), Siberian Branch of the Russian Academy of Sciences, Novosibirsk
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Abstract: In this paper, a step-by-step modification of a well-known approach of Mikhailenko and Konyukh for solving dynamic problems is proposed. The approach is based on the Laguerre transform with respect to time. In this modification the Laguerre transform is applied to a sequence of finite time intervals. The solution obtained at the end of a time interval is used as the initial data for problem solving on the next time interval. The method is illustrated by the examples of a harmonic oscillator problem and a 1D wave equation. The accuracy and stability of the method are analyzed. This approach allows obtaining a solution of high accuracy on large time intervals.
Key words: dynamic problems, Laguerre transformation, step-by-step method, accuracy, stability.
Received: 09.09.2009
Revised: 10.12.2009
English version:
Numerical Analysis and Applications, 2010, Volume 3, Issue 4, Pages 336–343
DOI: https://doi.org/10.1134/S1995423910040051
Bibliographic databases:
Document Type: Article
UDC: 519.633.6+517.44
Language: Russian
Citation: G. V. Demidov, V. N. Martynov, “A step-by-step method with Laguerre functions for solving time-dependent problems”, Sib. Zh. Vychisl. Mat., 13:4 (2010), 413–422; Num. Anal. Appl., 3:4 (2010), 336–343
Citation in format AMSBIB
\Bibitem{DemMar10}
\by G.~V.~Demidov, V.~N.~Martynov
\paper A step-by-step method with Laguerre functions for solving time-dependent problems
\jour Sib. Zh. Vychisl. Mat.
\yr 2010
\vol 13
\issue 4
\pages 413--422
\mathnet{http://mi.mathnet.ru/sjvm416}
\transl
\jour Num. Anal. Appl.
\yr 2010
\vol 3
\issue 4
\pages 336--343
\crossref{https://doi.org/10.1134/S1995423910040051}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-78650347646}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Sibirskii Zhurnal Vychislitel'noi Matematiki
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