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

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

\theta

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-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

\theta

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. 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.

Keywords

Space-fractional delay Fisher equation / Grünwald-Letnikov operator /

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-method')">Linear

\theta

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-method / Stability / Convergence

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Funding

National Natural Science Foundation of China(11201084)

RIGHTS & PERMISSIONS

Shanghai University