Numerical method and analytical technique of the modified anomalous subdiffusion equation with a nonlinear source term

Authors:
F. Liu;C. Yang;K. Burrage
Affiliations:
School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Qld. 4001, Australia and IMB, University of Queensland, Qld. 4072, Australia;School of Mathematical Sciences, Xiamen University, Xiamen 361005, China;IMB, University of Queensland, Qld. 4072, Australia and COMLAB, Oxford University, OX1 3LB, UK and OCISB, Oxford University, OX1 3LB, UK
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

In this paper, we consider a modified anomalous subdiffusion equation with a nonlinear source term for describing processes that become less anomalous as time progresses by the inclusion of a second fractional time derivative acting on the diffusion term. A new implicit difference method is constructed. The stability and convergence are discussed using a new energy method. Finally, some numerical examples are given. The numerical results demonstrate the effectiveness of theoretical analysis.