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 publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages44-55
Number of pages12
Volume5434 LNCS
DOIs
Publication statusPublished - 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)03029743
ISSN (Electronic)16113349

Other

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

Fingerprint

Crank-Nicolson Method
Heat Conduction Equation
Qualitative Properties
Qualitative Analysis
Heat conduction
Discretization
Crank-Nicolson
Heat Conduction
Preservation
Finite Difference
Numerical Solution
Finite Element
Requirements

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Faragó, I. (2009). Qualitative analysis of the Crank-Nicolson method for the heat conduction equation. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5434 LNCS, 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

Qualitative analysis of the Crank-Nicolson method for the heat conduction equation. / Faragó, I.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 5434 LNCS 2009. p. 44-55 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5434 LNCS).

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

Faragó, I 2009, Qualitative analysis of the Crank-Nicolson method for the heat conduction equation. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 5434 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5434 LNCS, pp. 44-55, 4th International Conference on Numerical Analysis and Its Applications, NAA 2008, Lozenetz, Bulgaria, 6/16/08. https://doi.org/10.1007/978-3-642-00464-3-5
Faragó I. Qualitative analysis of the Crank-Nicolson method for the heat conduction equation. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 5434 LNCS. 2009. p. 44-55. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-00464-3-5
Faragó, I. / Qualitative analysis of the Crank-Nicolson method for the heat conduction equation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 5434 LNCS 2009. pp. 44-55 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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