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The Scientific World Journal
Volume 2014, Article ID 681707, 5 pages
http://dx.doi.org/10.1155/2014/681707
Research Article

A Domain Decomposition Method for Time Fractional Reaction-Diffusion Equation

1College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China
2Science and Technology on Space Physics Laboratory, Beijing 100076, China
3School of Computer Science, National University of Defense Technology, Changsha 410073, China
4Department of Engineering Science, University of Oxford, Oxford OX2 0ES, UK

Received 21 December 2013; Accepted 20 February 2014; Published 19 March 2014

Academic Editors: A. Atangana, S. C. O. Noutchie, and A. Secer

Copyright © 2014 Chunye Gong et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The computational complexity of one-dimensional time fractional reaction-diffusion equation is compared with for classical integer reaction-diffusion equation. Parallel computing is used to overcome this challenge. Domain decomposition method (DDM) embodies large potential for parallelization of the numerical solution for fractional equations and serves as a basis for distributed, parallel computations. A domain decomposition algorithm for time fractional reaction-diffusion equation with implicit finite difference method is proposed. The domain decomposition algorithm keeps the same parallelism but needs much fewer iterations, compared with Jacobi iteration in each time step. Numerical experiments are used to verify the efficiency of the obtained algorithm.