ORIGINAL PAPERS

Numerical Stability and Convergence for Delay Space-Fractional Fisher Equations with Mixed Boundary Conditions in Two Dimensions

  • Jing Chen ,
  • Qi Wang
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  • School of Mathematics and Statistics, Guangdong University of Technology, Guangzhou, 510006, Guangdong, China

Received date: 2023-06-26

  Revised date: 2023-09-14

  Accepted date: 2023-10-23

  Online published: 2024-02-05

Supported by

This work is supported by the National Natural Science Foundation of China (No. 11201084).

Abstract

In this paper, for generalized two-dimensional delay space-fractional Fisher equations with mixed boundary conditions, we present the stability and convergence computed by a novel numerical method. The unconditional stability of analytic solutions is first derived. Next, we have established the linear θ-method with the Grünwald-Letnikov operator, which has the first-order accuracy in spatial dimensions. Moreover, approaches involved error estimations and inequality reductions are utilized to prove the stability and convergence of numerical solutions under different values of θ. Eventually, we implement a numerical experiment to validate theoretical conclusions, where the interaction impacts of fractional derivatives have been further analyzed by applying two different harmonic operators.

Cite this article

Jing Chen , Qi Wang . Numerical Stability and Convergence for Delay Space-Fractional Fisher Equations with Mixed Boundary Conditions in Two Dimensions[J]. Communications on Applied Mathematics and Computation, 2025 , 7(4) : 1462 -1488 . DOI: 10.1007/s42967-023-00346-x

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