Communications on Applied Mathematics and Computation >

2025 , Vol. 7 >Issue 1: 315 - 346

DOI: https://doi.org/10.1007/s42967-023-00282-w

Numerical Approach for Solving Two-Dimensional Time-Fractional Fisher Equation via HABC-N Method

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  • Institute of Information and Computation, School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China

Received date: 2023-02-21

  Revised date: 2023-04-19

  Accepted date: 2023-05-02

  Online published: 2025-04-21

Supported by

LW is supported by the National Natural Science Foundation of China (No.11371135) and the Fundamental Research Funds for the Central Universities (No.2021MS045).

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Abstract

For the two-dimensional time-fractional Fisher equation (2D-TFFE), a hybrid alternating band Crank-Nicolson (HABC-N) method based on the parallel finite difference technique is proposed. The explicit difference method, implicit difference method, and C-N difference method are used simultaneously with the alternating band technique to create the HABC-N method. The existence of the solution and unconditional stability for the HABC-N method, as well as its uniqueness, are demonstrated by theoretical study. The HABC-N method’s convergence order is O(τ2-α + h12 + h22). The theoretical study is bolstered by numerical experiments, which establish that the 2D-TFFE can be solved using the HABC-N method.

Key words： Two-dimensional time-fractional Fisher equation (2D-TFFE); Hybrid alternating band Crank-Nicolson (HABC-N) method; Unconditional stability; Convergence order; Parallel computing

Cite this article

Ren Liu, Lifei Wu . Numerical Approach for Solving Two-Dimensional Time-Fractional Fisher Equation via HABC-N Method[J]. Communications on Applied Mathematics and Computation, 2025 , 7(1) : 315 -346 . DOI: 10.1007/s42967-023-00282-w

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