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Moving Finite Element Methods for a System of Semi-Linear Fractional Diffusion Equations

Part of: Partial differential equations, initial value and time-dependent initial-boundary value problems Integral equations, integral transforms Miscellaneous topics - Partial differential equations

Published online by Cambridge University Press:  19 September 2016

Jingtang Ma  and
Zhiqiang Zhou
Jingtang Ma*
Affiliation:
School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, China
Zhiqiang Zhou*
Affiliation:
School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, China
*
*Corresponding author. Email:mjt@swufe.edu.cn (J. T. Ma), zqzhou@2014.swufe.edu.cn (Z. Q. Zhou)
*Corresponding author. Email:mjt@swufe.edu.cn (J. T. Ma), zqzhou@2014.swufe.edu.cn (Z. Q. Zhou)
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Abstract

This paper studies a system of semi-linear fractional diffusion equations which arise in competitive predator-prey models by replacing the second-order derivatives in the spatial variables with fractional derivatives of order less than two. Moving finite element methods are proposed to solve the system of fractional diffusion equations and the convergence rates of the methods are proved. Numerical examples are carried out to confirm the theoretical findings. Some applications in anomalous diffusive Lotka-Volterra and Michaelis-Menten-Holling predator-prey models are studied.

Keywords

Finite element methodsfractional differential equationspredator-prey models

MSC classification

Secondary: 65M60: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 65M12: Stability and convergence of numerical methods 65M06: Finite difference methods 35S10: Initial value problems for pseudodifferential operators 65R20: Integral equations

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Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 8 , Issue 6 , December 2016 , pp. 911 - 931
Copyright
Copyright © Global-Science Press 2016 

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