Operator splitting and approximate factorization for taxis-diffusion-reaction models
Applied Numerical Mathematics
Numerical methods for the solution of partial differential equations of fractional order
Journal of Computational Physics
Numerical solution of the space fractional Fokker-Planck equation
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the international conference on boundary and interior layers - computational and asymptotic methods (BAIL 2002)
Finite difference approximations for fractional advection-dispersion flow equations
Journal of Computational and Applied Mathematics
Finite difference approximations for two-sided space-fractional partial differential equations
Applied Numerical Mathematics
Finite difference methods for two-dimensional fractional dispersion equation
Journal of Computational Physics
A second-order accurate numerical approximation for the fractional diffusion equation
Journal of Computational Physics
Journal of Computational and Applied Mathematics
A second-order accurate numerical method for the two-dimensional fractional diffusion equation
Journal of Computational Physics
Least squares finite-element solution of a fractional order two-point boundary value problem
Computers & Mathematics with Applications
Trotter products and reaction-diffusion equations
Journal of Computational and Applied Mathematics
A direct O(Nlog2N) finite difference method for fractional diffusion equations
Journal of Computational Physics
Numerical Schemes with High Spatial Accuracy for a Variable-Order Anomalous Subdiffusion Equation
SIAM Journal on Scientific Computing
Multigrid method for fractional diffusion equations
Journal of Computational Physics
A circulant preconditioner for fractional diffusion equations
Journal of Computational Physics
Convergence analysis of moving finite element methods for space fractional differential equations
Journal of Computational and Applied Mathematics
Preconditioned iterative methods for fractional diffusion equation
Journal of Computational Physics
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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.