Baeumer, Boris; Kovács, Mihály; Meerschaert, Mark M. Numerical solutions for fractional reaction-diffusion equations. (English) Zbl 1142.65422 Comput. Math. Appl. 55, No. 10, 2212-2226 (2008). 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. Cited in 83 Documents MSC: 65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems 35K57 Reaction-diffusion equations Keywords:fractional reaction-diffusion; operator semigroups; operator splitting; infinitely divisible distributions; invasive species Software:STABLE × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Britton, N. F., Reaction-Diffusion Equations and Their Applications to Biology (1986), Academic Press Inc. [Harcourt Brace Jovanovich Publishers]: Academic Press Inc. [Harcourt Brace Jovanovich Publishers] London · Zbl 0602.92001 [2] Cantrell, R. 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