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Zbl 1142.65422
Baeumer, Boris; Kovács, Mihály; Meerschaert, Mark M.
Numerical solutions for fractional reaction-diffusion equations. (English)
[J] Comput. Math. Appl. 55, No. 10, 2212-2226 (2008). ISSN 0898-1221

Summary: Fractional diffusion equations are useful for applications in which a cloud of particles spreads faster than predicted by the classical equation. In a fractional diffusion equation, the second derivative in the spatial variable is replaced by a fractional derivative of order less than two. The resulting solutions spread faster than the classical solutions and may exhibit asymmetry, depending on the fractional derivative used. Fractional reaction-diffusion equations combine the fractional diffusion with a classical reaction term. In this paper, we develop a practical method for numerical solution of fractional reaction-diffusion equations, based on operator splitting. Then we present results of numerical simulations to illustrate the method, and investigate properties of numerical solutions. We also discuss applications to biology, where the reaction term models species growth and the diffusion term accounts for movements.

MSC 2000:: *65M99 Numerical methods for IVP of PDE
35K57 Reaction-diffusion equations

Keywords: fractional reaction-diffusion; operator semigroups; operator splitting; infinitely divisible distributions; invasive species

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Zentralblatt MATH Berlin [Germany]