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.
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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|Item Type:||Journal Article|
|Keywords:||alternating direction implicit method, Legendre spectral method, Riesz space fractional reaction-diffusion equation, fractional FitzHugh–Nagumo model, stability and convergence|
|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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