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

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 $O\left( {\tau ^{2 - \alpha }} + h_1^2 + h_2^2\right)$. The theoretical study is bolstered by numerical experiments, which establish that the 2D-TFFE can be solved using the HABC-N method.

Keywords

Two-dimensional time-fractional Fisher equation (2D-TFFE) / Hybrid alternating band Crank-Nicolson (HABC-N) method / Unconditional stability / Convergence order / Parallel computing / 65M06 (Finite difference methods for initial value and initial-boundary value problems involving PDEs) / 65M12 (Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs) / 65Y05 (Parallel numerical computation)

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Funding

National Natural Science Foundation of China(11371135)

Fundamental Research Funds for the Central Universities(2021MS045)

RIGHTS & PERMISSIONS

Shanghai University