Numerical Solution of Parabolic Problems with Nonlocal Boundary Conditions

In this article, the one-dimensional parabolic equation with three types of integral nonlocal boundary conditions is approximated by the implicit Euler finite difference scheme. Stability analysis is done in the maximum norm and it is proved that the radius of the stability region and the stiffness...

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Bibliographic Details
Published inNumerical functional analysis and optimization Vol. 31; no. 12; pp. 1318 - 1329
Main Authors Čiegis, R., Tumanova, N.
Format Journal Article
LanguageEnglish
Published Taylor & Francis Group 19.11.2010
Subjects
Approximation
Boundary conditions
Convergence
Convergence analysis
Finite difference method
Integrals
Mathematical analysis
Mathematical models
Nonlocal boundary conditions
Norms
Parabolic problems
Regularization
Stability
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ISSN0163-0563
1532-2467
DOI10.1080/01630563.2010.526734

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Summary:In this article, the one-dimensional parabolic equation with three types of integral nonlocal boundary conditions is approximated by the implicit Euler finite difference scheme. Stability analysis is done in the maximum norm and it is proved that the radius of the stability region and the stiffness of the discrete scheme depends on the signs of coefficients in the nonlocal boundary condition. The known stability results are improved. In the case of a plain integral boundary condition, the conditional convergence rate is proved and the regularization relation between discrete time and space steps is proposed. The accuracy of the obtained estimates is illustrated by results of numerical experiments.
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ISSN:0163-0563
1532-2467
DOI:10.1080/01630563.2010.526734