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Paper   IPM / M / 8287
School of Mathematics
  Title:   A computational study of the one-dimensional parabolic equation subject to nonclassical boundary specifications
  Author(s):  M. Dehghan
  Status:   Published
  Journal: Numer. Methods Partial Differential Eq.
  Vol.:  22
  Year:  2006
  Pages:   220-257
  Supported by:  IPM
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 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 nonclassical boundary value problem. To investigate the performance of the proposed algorithm, we consider solving a test problem.

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