Two novel numerical methods for solving the two-dimensional fractional Fitzhugh-Nagumo-monodomain model
Burrage, K., Liu, F., Turner, I., & Anh, V. (2012) Two novel numerical methods for solving the two-dimensional fractional Fitzhugh-Nagumo-monodomain model. In Turner, Ian (Chair) (Ed.) The 16th Biennial Computational Techniques and Applications Conference, 23 - 26 September, 2012, Brisbane, Queensland.
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Fractional mathematical models represent a new approach to modelling complex spatial problems in which there is heterogeneity at many spatial and temporal scales. In this paper, a two-dimensional fractional Fitzhugh-Nagumo-monodomain model with zero Dirichlet boundary conditions is considered. The model consists of a coupled space fractional diffusion equation (SFDE) and an ordinary differential equation. For the SFDE, we first consider the numerical solution of the Riesz fractional nonlinear reaction-diffusion model and compare it to the solution of a fractional in space nonlinear reaction-diffusion model. We present two novel numerical methods for the two-dimensional fractional Fitzhugh-Nagumo-monodomain model using the shifted Grunwald-Letnikov method and the matrix transform method, respectively. Finally, some numerical examples are given to exhibit the consistency of our computational solution methodologies. The numerical results demonstrate the effectiveness of the methods.
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|Item Type:||Conference Item (Presentation)|
|Divisions:||Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
|Copyright Owner:||Copyright 2012 all authors|
|Deposited On:||15 May 2013 23:29|
|Last Modified:||21 May 2013 05:41|
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