On Stability Analysis of Finite-Difference Schemes for Some Parabolic Problems with Nonlocal Boundary Conditions

In this article, one-dimensional parabolic and pseudo-parabolic equations with nonlocal boundary conditions are approximated by the implicit Euler finite-difference scheme. For a parabolic problem, the stability analysis is done in the weak H −1 type norm, which enables us to generalize results obta...

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Bibliographic Details
Published inNumerical functional analysis and optimization Vol. 35; no. 10; pp. 1308 - 1327
Main Authors Čiegis, Raimondas, Jankevičiūtė, Gerda, Leonavičienė, Teresė, Mirinavičius, Aleksas
Format Journal Article
LanguageEnglish
Published Taylor & Francis Group 03.10.2014
Subjects
Convergence analysis
Finite-difference method
Nonlocal boundary conditions
Parabolic problem
Pseudo-parabolic problem
Stability
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ISSN0163-0563
1532-2467
DOI10.1080/01630563.2014.908208

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Summary:In this article, one-dimensional parabolic and pseudo-parabolic equations with nonlocal boundary conditions are approximated by the implicit Euler finite-difference scheme. For a parabolic problem, the stability analysis is done in the weak H −1 type norm, which enables us to generalize results obtained in stronger norms. In the case of a pseudo-parabolic problem, the stability analysis is done in the discrete analog of the norm. It is shown that a solution of the proposed finite-discrete scheme satisfies stronger stability estimates than a discrete solution of the parabolic problem. Results of numerical experiments are presented.
ISSN:0163-0563
1532-2467
DOI:10.1080/01630563.2014.908208