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2013 | 11 | 10 | 1221-1232
Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
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.
Wydawca

Czasopismo
Rocznik
Tom
11
Numer
10
Strony
1221-1232
Opis fizyczny
Daty
wydano
2013-10-01
online
2013-12-19
Twórcy
autor
  • School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Qld., 4001, Australia, f.liu@qut.edu.au
autor
  • Department of Mathematics, Quanzhou Normal University, Quanzhou, Fujian, China
autor
  • School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Qld., 4001, Australia
autor
  • School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Qld., 4001, Australia
Bibliografia
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Typ dokumentu
Bibliografia
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