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

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  • Department of Mathematics, Shanghai University, Shanghai 200444, China

Received date: 2022-11-24

  Revised date: 2022-12-08

  Online published: 2023-12-16

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.

Cite this article

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

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