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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2011, Volume 14, Number 4, Pages 361–379 (Mi sjvm448)  
This article is cited in 6 scientific papers (total in 6 papers)

Implicit difference methods for evolution functional differential equations

Z. Kamont, K. Kropielnicka

Institute of Mathematics, University of Gdańsk, Gdańsk, Poland
Full-text PDF (277 kB) Citations (6)
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Abstract: A general theory of implicit difference schemes for nonlinear functional differential equations with initial boundary conditions is presented.
A theorem on error estimates of approximate solutions for implicit functional difference equations of the Volterra type with an unknown function of several variables is given. This general result is employed to investigate the stability of implicit difference schemes generated by first-order partial differential functional equations and by parabolic problems. A comparison technique with nonlinear estimates of the Perron type for given functions with respect to the functional variable is used.
Key words: functional differential equations, implicit difference methods, stability and convergence.
Received: 21.09.2010
English version:
Numerical Analysis and Applications, 2011, Volume 4, Issue 4, Pages 294–308
DOI: https://doi.org/10.1134/S1995423911040033
Bibliographic databases:
Document Type: Article
MSC: 65M12, 35R10
Language: Russian
Citation: Z. Kamont, K. Kropielnicka, “Implicit difference methods for evolution functional differential equations”, Sib. Zh. Vychisl. Mat., 14:4 (2011), 361–379; Num. Anal. Appl., 4:4 (2011), 294–308
Citation in format AMSBIB
\Bibitem{KamKro11}
\by Z.~Kamont, K.~Kropielnicka
\paper Implicit difference methods for evolution functional differential equations
\jour Sib. Zh. Vychisl. Mat.
\yr 2011
\vol 14
\issue 4
\pages 361--379
\mathnet{http://mi.mathnet.ru/sjvm448}
\transl
\jour Num. Anal. Appl.
\yr 2011
\vol 4
\issue 4
\pages 294--308
\crossref{https://doi.org/10.1134/S1995423911040033}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84155189746}
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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