A novel compact ADI scheme for two-dimensional Riesz space fractional nonlinear reaction–diffusion equations

Xiujun Cheng, Jinqiao Duan and Dongfang Li

Applied Mathematics and Computation, 2019, vol. 346, issue C, 452-464

Abstract: This paper is concerned with the construction and analysis of a novel linearized compact ADI scheme for the two-dimensional Riesz space fractional nonlinear reaction–diffusion equations. Convergence of the proposed scheme is proved. The highlight is that the time discretization is achieved by applying a second-order, one-step and linearized method. The time discretization requires only one starting value, which is sharp contrast to the extrapolated Crank–Nicolson method or the usual second-order linearized schemes. Numerical examples on several fractional models are presented to confirm our theoretical results.

Keywords: Alternating direction implicit (ADI) method Riesz space fractional nonlinear Reaction–diffusion problem; Convergence (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (10)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:346:y:2019:i:c:p:452-464

DOI: 10.1016/j.amc.2018.10.065

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