A Fourth-Order ADI Compact Difference Scheme for the Two-Dimensional Space-Fractional Diffusion Equation With Different Tempering Parameters

Taiqiang Jiang, Xiaotong Li and Zeshan Qiu

Journal of Mathematics, 2026, vol. 2026, 1-13

Abstract: In this paper, we developed an improved fourth-order approximation for the Riemann–Liouville tempered fractional derivatives and applied it to solve the two-dimensional space-tempered fractional diffusion equation. The first-order temporal derivative was discretized using the Crank–Nicolson method, while the spatial tempered fractional derivatives were approximated by the improved fourth-order formula. The resulting two-dimensional discrete system was then handled by the alternating direction implicit (ADI) method to reduce computational cost. The stability and convergence of the numerical scheme were established. Numerical experiments were presented to validate the effectiveness of the proposed scheme.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:5708674

DOI: 10.1155/jom/5708674

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