A second-order numerical method for nonlinear variable-order fractional diffusion equation with time delay

Jing Li, Xinyue Kang, Xingyun Shi and Yufei Song

Mathematics and Computers in Simulation (MATCOM), 2024, vol. 219, issue C, 101-111

Abstract: In this paper, a linearized numerical scheme of nonlinear variable-order fractional diffusion equation with time delay is constructed. We apply the L2−1σ formula to discretize the temporal derivative and second-order central difference scheme to discretize the spatial derivative. The proposed method is unconditionally stable and convergent with Oτ2+h2, where τ and h are the time and space steps, respectively. Numerical experiment demonstrates the effectiveness and accuracy of the numerical scheme.

Keywords: Nonlinear variable-order diffusion equation; L2−1σ formula; Stability; Convergence (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:219:y:2024:i:c:p:101-111

DOI: 10.1016/j.matcom.2023.12.019

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