Finite Difference Schemes for Time-Space Fractional Diffusion Equations in One- and Two-Dimensions
Yu Wang , Min Cai
Communications on Applied Mathematics and Computation ›› 2023, Vol. 5 ›› Issue (4) : 1674 -1696.
Finite Difference Schemes for Time-Space Fractional Diffusion Equations in One- and Two-Dimensions
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.
National Natural Science Foundation of China(12201391)
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