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.

[img] Presentation (PDF 2MB)
Administrators only | Request a copy from author

View at publisher

Abstract

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.

Impact and interest:

Citation counts are sourced monthly from Scopus and Web of Science® citation databases.

These databases contain citations from different subsets of available publications and different time periods and thus the citation count from each is usually different. Some works are not in either database and no count is displayed. Scopus includes citations from articles published in 1996 onwards, and Web of Science® generally from 1980 onwards.

Citations counts from the Google Scholar™ indexing service can be viewed at the linked Google Scholar™ search.

ID Code: 60001
Item Type: Conference Item (Presentation)
Refereed: Yes
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

Export: EndNote | Dublin Core | BibTeX

Repository Staff Only: item control page