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

Yu Wang; Min Cai

doi:10.1007/s42967-022-00244-8

Communications on Applied Mathematics and Computation ›› 2023, Vol. 5 ›› Issue (4) : 1674-1696. DOI: 10.1007/s42967-022-00244-8

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

Yu Wang¹ ,
Min Cai¹^,b

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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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Yu Wang, Min Cai. Finite Difference Schemes for Time-Space Fractional Diffusion Equations in One- and Two-Dimensions. Communications on Applied Mathematics and Computation, 2023, 5(4): 1674‒1696 https://doi.org/10.1007/s42967-022-00244-8