Numerical Methods for Partial Differential Equations · 2005 · 158 citations · 78 references
Natural SciencesComputational EngineeringComputational MechanicsDifferential EquationsFluid DynamicsBoundary ConditionsBoundary-value ProblemsFinite Difference MethodsNumerical Methods For Differential EquationsBoundary ProblemFinite Difference Solution Of Partial Differential EquationsInitial-boundary Value ProblemsNumerical Methods For Initial Value ProblemsParabolic Boundary-value ProblemsParabolic Equation ModelingParabolic Partial Differential Equations
Abstract 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
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