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Abstract
In this decade, many new applications in engineering and science are governed by a series of fractional partial differential equations. In this paper, we propose a novel numerical method for a class of time-dependent fractional partial differential equations. The time variable is discretized by using the second order backward differentiation formula scheme, and the quasi-wavelet method is used for spatial discretization. The stability and convergence properties related to the time discretization are discussed and theoretically proven. Numerical examples are obtained to investigate the accuracy and efficiency of the proposed method. The comparisons of the present numerical results with the exact analytical solutions show that the quasi-wavelet method has distinctive local property and can achieve accurate results.
Acknowledgements
We would like to thank the reviewers and the editors for their invaluable suggestions, and are grateful to Prof Da Xu and Dr Xuehua Yang from Hunan Normal University for their assistance during the preparation of this paper. This research was partially supported by the Research and Innovation Project for College Graduates of Hunnan Province CX2012B196.
Project supported by the National Nature Science Foundation of China (nos. 11271376, 60970097, and 41204082).