A computational study of the one-dimensional parabolic equation subject to nonclassical boundary specifications

Certain problems arising in engineering are modeled by nonstandard parabolic initial‐boundary value problems in one space variable, which involve an integral term over the spatial domain of a function of the desired solution. Hence, in the past few years interest has substantially increased in the s...

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Veröffentlicht in:Numerical methods for partial differential equations Jg. 22; H. 1; S. 220 - 257
1. Verfasser: Dehghan, Mehdi
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Hoboken Wiley Subscription Services, Inc., A Wiley Company 01.01.2006
Schlagworte:
boundary element method
decomposition method
double shifted Legendre series
existence
explicit schemes
finite difference schemes
Galerkin procedure
implicit techniques
Keller-box scheme
Legendre Tau method
nonstandard boundary value problems
numerical integration
orthogonal spline collocation
pade approximant
parallel algorithms
product integration method
representation of solutions
Runge-Kutta-Chebyshev formula
second-order parabolic equation
semidiscretization techniques
separation of variables
stability
uniqueness
wavelet-Galerkin technique
ISSN:0749-159X, 1098-2426
Online-Zugang:Volltext
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Zusammenfassung:Certain problems arising in engineering are modeled by nonstandard parabolic initial‐boundary value problems in one space variable, which involve an integral term over the spatial domain of a function of the desired solution. Hence, in the past few years interest has substantially increased in the solutions of these problems. As a result numerous research papers have also been devoted to the subject. Although considerable amount of work has been done in the past, there is still a lack of a completely satisfactory computational scheme. Also, there are some cases that have not been studied numerically yet. In the current article several approaches for the numerical solution of the one‐dimensional parabolic equation subject to the specification of mass, which have been considered in the literature, are reported. Finite difference methods have been proposed for the numerical solution of the new nonclassic boundary value problem. To investigate the performance of the proposed algorithm, we consider solving a test problem. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006
Bibliographie:ark:/67375/WNG-DKB3R60J-Z
Institute for Studies in Theoretical Physics and Mathematics (IPM), Tehran, Iran - No. 84650030
istex:9795E77FDBC1AC179112F6CD427AC569BF0DEE2F
ArticleID:NUM20071
ISSN:0749-159X
1098-2426
DOI:10.1002/num.20071