A Crank--Nicolson ADI spectral method for a two-dimensional riesz space fractional nonlinear reaction-diffusion equation

Zeng, Fanhai, Liu, Fawang, Li, Changpin, Burrage, Kevin, Turner, Ian, & Anh, V. (2014) A Crank--Nicolson ADI spectral method for a two-dimensional riesz space fractional nonlinear reaction-diffusion equation. SIAM Journal on Numerical Analysis, 52(6), pp. 2599-2622.

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Abstract

In this paper, a new alternating direction implicit Galerkin--Legendre spectral method for the two-dimensional Riesz space fractional nonlinear reaction-diffusion equation is developed. The temporal component is discretized by the Crank--Nicolson method. The detailed implementation of the method is presented. The stability and convergence analysis is strictly proven, which shows that the derived method is stable and convergent of order $2$ in time. An optimal error estimate in space is also obtained by introducing a new orthogonal projector. The present method is extended to solve the fractional FitzHugh--Nagumo model. Numerical results are provided to verify the theoretical analysis.

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ID Code: 82655
Item Type: Journal Article
Refereed: Yes
Keywords: alternating direction implicit method, Legendre spectral method, Riesz space fractional reaction-diffusion equation, fractional FitzHugh–Nagumo model, stability and convergence
DOI: 10.1137/130934192
ISSN: 1095-7170
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200) > Dynamical Systems in Applications (010204)
Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > NUMERICAL AND COMPUTATIONAL MATHEMATICS (010300)
Divisions: Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2014, Society for Industrial and Applied Mathematics
Deposited On: 23 Mar 2015 00:06
Last Modified: 23 Mar 2015 21:30

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