ABOUT THE CONVERGENCE OF A NUMERICAL
SCHEME OF HIGH ORDER TO SOLVE FRACTIONAL
REACTION-SUBDIFFUSION EQUATION
Jorge Andrés Julca Avila1, Aurelio José Parreira2,
Juan Carlos Zavaleta Aguilar3
1,2,3Department of Mathematics and Statistics
Federal University of São João del-Rei
São João del-Rei, MG, 36307-904, BRAZIL
Abstract. In this work the anomalous diffusion phenomenon with reaction was modeled by Temporal Fractional Partial Differential Equation. The convergence of high order implicit numerical scheme for one-dimension reaction-subdiffusion equation was analyzed. Fort this, we used the Implicit Compact Finite Difference Method for discretization of spacial variable and Backward Finite Difference for temporal variable. For the Riemann-Liouville's temporal fractional derivative we used the Grunwald-Letnikov's discretization. Finally, we proved the convergence order using an example and numerical tests.
AMS Subject classification: 65N12
Keywords and phrases: anomalous diffusion, compact finite difference, fractional differential partial equation, high order of numerical scheme, continuous time random walk


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DOI: 10.12732/ijam.v27i4.5

Volume: 27
Issue: 4
Year: 2014