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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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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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
Keywords
- Time-fractional subdiffusion equation
- Convolution quadrature
- Fractional linear multistep methods
- Discrete fractional Grönwall inequality
- Unconditional stability