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

doi:10.1007/s42967-023-00282-w

Abstract

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(τ^2-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

CLC Number:

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.

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