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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Vydané v:	Numerical methods for partial differential equations Ročník 22; číslo 1; s. 220 - 257
Hlavný autor:	Dehghan, Mehdi
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Hoboken Wiley Subscription Services, Inc., A Wiley Company 01.01.2006
Predmet:	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
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Popis
Shrnutí:	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
Bibliografia:	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