The ANZIAM Journal · 2008 · 27 citations · 19 references
Natural SciencesMathematicsPhysicsComputational PhysicsDifferential EquationsReaction EngineeringFinite Difference MethodsFourier AnalysisFourier Series MethodsLaplace Transform MethodsNumerical Methods For Differential EquationsFinite Difference ApproximationFinite Difference SchemesFinite Difference Solution Of Partial Differential EquationsFractional Differential EquationsFundamental SolutionsRiesz Operators
Abstract A Riesz space-fractional reaction–dispersion equation (RSFRDE) is obtained from the classical reaction–dispersion equation (RDE) by replacing the second-order space derivative with a Riesz derivative of order β ∈(1,2]. In this paper, using Laplace and Fourier transforms, we obtain the fundamental solution for a RSFRDE. We propose an explicit finite-difference approximation for a RSFRDE in a bounded spatial domain, and analyse its stability and convergence. Some numerical examples are presented.
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