Numerical simulation for two-dimensional Riesz space fractional diffusion equations with a nonlinear reaction term

• Authors: Fawang Liu , Shiping Chen , Ian Turner , Kevin Burrage , Vo Anh
• Languages of publication: EN

Abstracts

EN

Fractional differential equations have attracted considerable interest because of their ability to model anomalous transport phenomena. Space fractional diffusion equations with a nonlinear reaction term have been presented and used to model many problems of practical interest. In this paper, a two-dimensional Riesz space fractional diffusion equation with a nonlinear reaction term (2D-RSFDE-NRT) is considered. A novel alternating direction implicit method for the 2D-RSFDE-NRT with homogeneous Dirichlet boundary conditions is proposed. The stability and convergence of the alternating direction implicit method are discussed. These numerical techniques are used for simulating a two-dimensional Riesz space fractional Fitzhugh-Nagumo model. Finally, a numerical example of a two-dimensional Riesz space fractional diffusion equation with an exact solution is given. The numerical results demonstrate the effectiveness of the methods. These methods and techniques can be extended in a straightforward method to three spatial dimensions, which will be the topic of our future research.

Keywords

EN

fractional diffusion equation; alternating direct method; nonlinear reaction term; Fitzhugh-Nagumo model; Riesz space fractional derivative; stability and convergence

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2013
• Volume: 11
• Issue: 10
• Pages: 1221-1232

Dates

published

1 - 10 - 2013

online

19 - 12 - 2013

Contributors

author

Fawang Liu

• School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Qld., 4001, Australia

author

Shiping Chen

• Department of Mathematics, Quanzhou Normal University, Quanzhou, Fujian, China

author

Ian Turner

• School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Qld., 4001, Australia

author

Kevin Burrage

author

Vo Anh

• School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Qld., 4001, Australia

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Identifiers

DOI

10.2478/s11534-013-0296-z