Moving finite element methods for a system of semi-linear fractional diffusion equations. (English) Zbl 1488.65447
Summary: 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.
MSC:
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 35S10 | Initial value problems for PDEs with pseudodifferential operators |
| 65R20 | Numerical methods for integral equations |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 92D25 | Population dynamics (general) |
| 92-08 | Computational methods for problems pertaining to biology |
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
| 26A33 | Fractional derivatives and integrals |
| 35R11 | Fractional partial differential equations |
Software:
FODEReferences:
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