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Numerical Analysis of Linear and Nonlinear Time-Fractional Subdiffusion Equations

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Abstract

In this paper, a new type of the discrete fractional Grönwall inequality is developed, which is applied to analyze the stability and convergence of a Galerkin spectral method for a linear time-fractional subdiffusion equation. Based on the temporal–spatial error splitting argument technique, the discrete fractional Grönwall inequality is also applied to prove the unconditional convergence of a semi-implicit Galerkin spectral method for a nonlinear time-fractional subdiffusion equation.

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Acknowledgements

The authors wish to thank the referees for their constructive comments and suggestions, which greatly improved the quality of this paper.

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Authors and Affiliations

  1. Nanhu College, Jiaxing University, Jiaxing, 314001, Zhejiang, China

    Yubo Yang

  2. Department of Mathematics, National University of Singapore, Singapore, 119076, Singapore

    Fanhai Zeng

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  1. Yubo Yang
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  2. Fanhai Zeng
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Correspondence to Fanhai Zeng.

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Yang, Y., Zeng, F. Numerical Analysis of Linear and Nonlinear Time-Fractional Subdiffusion Equations. Commun. Appl. Math. Comput. 1, 621–637 (2019). https://doi.org/10.1007/s42967-019-00033-w

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  • DOI: https://doi.org/10.1007/s42967-019-00033-w

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