A Crank--Nicolson ADI spectral method for a two-dimensional riesz space fractional nonlinear reaction-diffusion equation
Data(s) |
2014
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Resumo |
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. |
Formato |
application/pdf |
Identificador | |
Publicador |
Society for Industrial and Applied Mathematics |
Relação |
http://eprints.qut.edu.au/82655/8/82655_pubVer.pdf DOI:10.1137/130934192 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. |
Direitos |
Copyright 2014, Society for Industrial and Applied Mathematics |
Fonte |
School of Mathematical Sciences; Science & Engineering Faculty |
Palavras-Chave | #010204 Dynamical Systems in Applications #010300 NUMERICAL AND COMPUTATIONAL MATHEMATICS #alternating direction implicit method, Legendre spectral method, Riesz space fractional reaction-diffusion equation, fractional FitzHugh–Nagumo model, stability and convergence |
Tipo |
Journal Article |