Volume 8, Issue 6
Moving Finite Element Methods for a System of Semi-Linear Fractional Diffusion Equations

Jingtang Ma & Zhiqiang Zhou

Adv. Appl. Math. Mech., 8 (2016), pp. 911-931.

Published online: 2018-05

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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 methods, fractional differential equations, predator-prey models.

  • AMS Subject Headings

65M60, 65M12, 65M06, 35S10, 65R20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-8-911, author = {Jingtang Ma , and Zhou , Zhiqiang}, title = {Moving Finite Element Methods for a System of Semi-Linear Fractional Diffusion Equations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {8}, number = {6}, pages = {911--931}, 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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2015.m1065}, url = {http://global-sci.org/intro/article_detail/aamm/12123.html} }
TY - JOUR T1 - Moving Finite Element Methods for a System of Semi-Linear Fractional Diffusion Equations AU - Jingtang Ma , AU - Zhou , Zhiqiang JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 911 EP - 931 PY - 2018 DA - 2018/05 SN - 8 DO - http://doi.org/10.4208/aamm.2015.m1065 UR - https://global-sci.org/intro/article_detail/aamm/12123.html KW - Finite element methods, fractional differential equations, predator-prey models. AB -

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.

Jingtang Ma & Zhiqiang Zhou. (2020). Moving Finite Element Methods for a System of Semi-Linear Fractional Diffusion Equations. Advances in Applied Mathematics and Mechanics. 8 (6). 911-931. doi:10.4208/aamm.2015.m1065
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