Numerical approximation for a variable-order nonlinear reaction---subdiffusion equation

Authors:
Chang-Ming Chen;F. Liu;I. Turner;V. Anh;Y. Chen
Affiliations:
School of Mathematical Sciences, Xiamen University, Xiamen, China 361005;School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia 4001;School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia 4001;School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia 4001;School of Mathematical Sciences, Xiamen University, Xiamen, China 361005
Venue:
Numerical Algorithms
Year:
2013

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Abstract

Fractional reaction---subdiffusion equations are widely used in recent years to simulate physical phenomena. In this paper, we consider a variable-order nonlinear reaction---subdiffusion equation. A numerical approximation method is proposed to solve the equation. Its convergence and stability are analyzed by Fourier analysis. By means of the technique for improving temporal accuracy, we also propose an improved numerical approximation. Finally, the effectiveness of the theoretical results is demonstrated by numerical examples.