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Finite Difference Schemes for Time-Space Fractional Diffusion Equations in One- and Two-Dimensions

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Abstract

In this paper, finite difference schemes for solving time-space fractional diffusion equations in one dimension and two dimensions are proposed. The temporal derivative is in the Caputo-Hadamard sense for both cases. The spatial derivative for the one-dimensional equation is of Riesz definition and the two-dimensional spatial derivative is given by the fractional Laplacian. The schemes are proved to be unconditionally stable and convergent. The numerical results are in line with the theoretical analysis.

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Acknowledgements

The authors would like to thank Prof. Changpin Li for his valuable suggestions and pointing out several typos in an earlier version of this paper. This research was partially supported by the National Natural Science Foundation of China under Grant Nos. 12271339 and 12201391.

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  1. Yu Wang and Min Cai have contributed equally to this work.

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  1. Department of Mathematics, Shanghai University, Shanghai, 200444, China

    Yu Wang & Min Cai

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  1. Yu Wang
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  2. Min Cai
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Correspondence to Min Cai.

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Wang, Y., Cai, M. Finite Difference Schemes for Time-Space Fractional Diffusion Equations in One- and Two-Dimensions. Commun. Appl. Math. Comput. 5, 1674–1696 (2023). https://doi.org/10.1007/s42967-022-00244-8

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  • DOI: https://doi.org/10.1007/s42967-022-00244-8

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