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A novel compact numerical method for solving the two-dimensional non-linear fractional reaction-subdiffusion equation

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Abstract

In this paper, we consider the two-dimensional non-linear fractional reaction-subdiffusion equation. A novel compact numerical method which is second-order temporal accuracy and fourth-order spatial accuracy is derived. The stability and convergence of the compact numerical method have been discussed rigorously by means of the Fourier method. Finally, numerical examples are presented to show the effectiveness and the high-order accuracy of the compact numerical method.

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Authors and Affiliations

  1. School of Mathematics, Shandong University, Jinan, 250100, China

    Bo Yu & Xiaoyun Jiang

  2. School of Mathematics and Statistics, Shandong University, Weihai, Weihai, 264209, China

    Huanying Xu

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  1. Bo Yu
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  2. Xiaoyun Jiang
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  3. Huanying Xu
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Correspondence to Xiaoyun Jiang.

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Yu, B., Jiang, X. & Xu, H. A novel compact numerical method for solving the two-dimensional non-linear fractional reaction-subdiffusion equation. Numer Algor 68, 923–950 (2015). https://doi.org/10.1007/s11075-014-9877-1

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  • DOI: https://doi.org/10.1007/s11075-014-9877-1

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