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

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 wit...

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Vydané v:Communications on Applied Mathematics and Computation (Online) Ročník 7; číslo 1; s. 315 - 346
Hlavní autori: Liu, Ren, Wu, Lifei
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Singapore Springer Nature Singapore 01.02.2025
Predmet:
Applications of Mathematics
Computational Science and Engineering
Mathematics
Mathematics and Statistics
Original Paper
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)
Unconditional stability
Two-dimensional time-fractional Fisher equation (2D-TFFE)
Hybrid alternating band Crank-Nicolson (HABC-N) method
65Y05 (Parallel numerical computation)
ISSN:2096-6385, 2661-8893
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Shrnutí: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 + h 1 2 + h 2 2 . The theoretical study is bolstered by numerical experiments, which establish that the 2D-TFFE can be solved using the HABC-N method.
ISSN:2096-6385
2661-8893
DOI:10.1007/s42967-023-00282-w