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

• Published in: Numerical methods for partial differential equations Vol. 22; no. 1; pp. 220 - 257
• Main Author: Dehghan, Mehdi
• Format: Journal Article
• Language: English
• Published: Hoboken Wiley Subscription Services, Inc., A Wiley Company 01.01.2006
• Subjects: 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
• DOI: 10.1002/num.20071

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