Matematicheskoe modelirovanie
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Matem. Mod.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Matematicheskoe modelirovanie, 2021, Volume 33, Number 4, Pages 60–78
DOI: https://doi.org/10.20948/mm-2021-04-04
(Mi mm4279)
 

This article is cited in 8 scientific papers (total in 8 papers)

Compact and monotone difference schemes for parabolic equations

P. P. Matusab, B. D. Utebaeva

a Institute of Mathematics of the National Academy of Sciences of Belarus, Minsk
b Institute of Mathematics and Computer Science the John Paul II Catholic University of Lublin, Lublin, Poland
Full-text PDF (413 kB) Citations (8)
References:
Abstract: In this paper, we consider compact and monotone difference schemes of the fourth order of approximation for linear, semilinear, and quasilinear equations of parabolic type. For the Fisher equation, the monotonicity, stability and convergence of the proposed methods are proved in the uniform norm $L_\infty$ or $C$. The results obtained are generalized to quasilinear parabolic equations with nonlinearities such as a porous medium. The work an abstract level defines the monotonicity of a difference scheme in the nonlinear case. The performed computational experiment illustrates the effectiveness of the considered methods. A way of determining the order of convergence of the proposed methods based on the Runge method in the case of the presence of several variables and different orders in different variables is indicated in the article.
Keywords: monotone difference schemes, maximum principle, compact difference schemes, two-side estimates.
Received: 06.07.2020
Revised: 30.11.2020
Accepted: 01.02.2021
English version:
Mathematical Models and Computer Simulations, 2021, Volume 13, Issue 6, Pages 1038–1048
DOI: https://doi.org/10.1134/S2070048221060132
Document Type: Article
Language: Russian
Citation: P. P. Matus, B. D. Utebaev, “Compact and monotone difference schemes for parabolic equations”, Matem. Mod., 33:4 (2021), 60–78; Math. Models Comput. Simul., 13:6 (2021), 1038–1048
Citation in format AMSBIB
\Bibitem{MatUte21}
\by P.~P.~Matus, B.~D.~Utebaev
\paper Compact and monotone difference schemes for parabolic equations
\jour Matem. Mod.
\yr 2021
\vol 33
\issue 4
\pages 60--78
\mathnet{http://mi.mathnet.ru/mm4279}
\crossref{https://doi.org/10.20948/mm-2021-04-04}
\transl
\jour Math. Models Comput. Simul.
\yr 2021
\vol 13
\issue 6
\pages 1038--1048
\crossref{https://doi.org/10.1134/S2070048221060132}
Linking options:
  • https://www.mathnet.ru/eng/mm4279
  • https://www.mathnet.ru/eng/mm/v33/i4/p60
  • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математическое моделирование
    Statistics & downloads:
    Abstract page:437
    Full-text PDF :165
    References:57
    First page:26
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024