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| Paper IPM / M / 8287 |
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| Abstract: | |
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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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