A high-order and unconditionally stable scheme for the modified anomalous fractional sub-diffusion equation with a nonlinear source term

Authors:
Akbar Mohebbi;Mostafa Abbaszadeh;Mehdi Dehghan
Affiliations:
Department of Applied Mathematics, Faculty of Mathematical Science, University of Kashan, Kashan, Iran;Department of Applied Mathematics, Faculty of Mathematical Science, University of Kashan, Kashan, Iran;Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Ave., 15914 Tehran, Iran
Venue:
Journal of Computational Physics
Year:
2013

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Abstract

The aim of this paper is to study the high order difference scheme for the solution of modified anomalous fractional sub-diffusion equation. The time fractional derivative is described in the Riemann-Liouville sense. In the proposed scheme we discretize the space derivative with a fourth-order compact scheme and use the Grunwald-Letnikov discretization of the Riemann-Liouville derivative to obtain a fully discrete implicit scheme. We analyze the solvability, stability and convergence of the proposed scheme using the Fourier method. The convergence order of method is O(@t+h^4). Numerical examples demonstrate the theoretical results and high accuracy of the proposed scheme.