A fourth-order compact solution of the two-dimensional modified anomalous fractional sub-diffusion equation with a nonlinear source term

Authors:
Mostafa Abbaszadeh;Akbar Mohebbi
Affiliations:
-;-
Venue:
Computers & Mathematics with Applications
Year:
2013

Citing 14
Cited 0

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Abstract

This work is concerned to the study of high order difference scheme for the solution of a two-dimensional modified anomalous sub-diffusion equation with a nonlinear source term which describes processes that become less anomalous as time progresses. The space fractional derivatives are described in the Riemann-Liouville sense. In the proposed scheme we discretize the space derivatives with a fourth-order compact scheme and use the Grunwald-Letnikov discretization of the Riemann-Liouville derivatives to obtain a fully discrete implicit scheme. We prove the stability and convergence of proposed scheme using the Fourier analysis. The convergence order of the proposed method is O(@t+h"x^4+h"y^4). Comparison of numerical results with analytical solutions demonstrates the unconditional stability and high accuracy of proposed scheme.