A Fourth Order Finite Difference Method for Time-Space Fractional Diffusion Equations
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Abstract
A finite difference method for a class of time-space fractional diffusion equations is considered. The trapezoidal formula and a fourth-order fractional compact difference scheme are, respectively, used in temporal and spatial discretisations and the method stability is studied. Theoretical estimates of the convergence in the L-2 -norm are shown to be O(tau(2) + h(4)), where tau and h are time and space mesh sizes. Numerical examples confirm theoretical results.
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Arshad, Sadia/0000-0001-9085-5915
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Keywords
Fractional Diffusion Equation, Riesz Derivative, High-Order Approximation, Stability, Convergence, fractional diffusion equation, convergence, Finite difference methods for initial value and initial-boundary value problems involving PDEs, high-order approximation, stability, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Fractional partial differential equations, Riesz derivative
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Citation
Arshad, Sadia...et al. (2018). "A Fourth Order Finite Difference Method for Time-Space Fractional Diffusion Equations", East Asian Journal on Applied Mathematics, Vol. 8, No. 4, pp. 764-781.
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1
Volume
8
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4
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764
End Page
781
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Scopus : 4
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