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

doi:10.1007/s42967-023-00346-x

摘要/Abstract

摘要： 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.

关键词: Space-fractional delay Fisher equation, Grünwald-Letnikov operator, Linear θ-method, Stability, Convergence

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.

Key words: Space-fractional delay Fisher equation, Grünwald-Letnikov operator, Linear θ-method, Stability, Convergence

中图分类号:

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.

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