Qualitative analysis of the Crank-Nicolson method for the heat conduction equation

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

The preservation of the basic qualitative properties - besides the convergence - is a basic requirement in the numerical solution process. For solving the heat conduction equation, the finite difference/linear finite element Crank-Nicolson type full discretization process is a widely used approach. In this paper we formulate the discrete qualitative properties and we also analyze the condition w.r.t. the discretization step sizes under which the different qualitative properties are preserved. We give exact conditions for the discretization of the one-dimensional heat conduction problem under which the basic qualitative properties are preserved.

Original languageEnglish
Title of host publicationNumerical Analysis and Its Applications - 4th International Conference, NAA 2008, Revised Selected Papers
Pages44-55
Number of pages12
DOIs
Publication statusPublished - Jul 20 2009
Event4th International Conference on Numerical Analysis and Its Applications, NAA 2008 - Lozenetz, Bulgaria
Duration: Jun 16 2008Jun 20 2008

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5434 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other4th International Conference on Numerical Analysis and Its Applications, NAA 2008
CountryBulgaria
CityLozenetz
Period6/16/086/20/08

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Faragó, I. (2009). Qualitative analysis of the Crank-Nicolson method for the heat conduction equation. In Numerical Analysis and Its Applications - 4th International Conference, NAA 2008, Revised Selected Papers (pp. 44-55). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5434 LNCS). https://doi.org/10.1007/978-3-642-00464-3-5