Matrix algorithms
Finite difference approximations for fractional advection-dispersion flow equations
Journal of Computational and Applied Mathematics
A second-order accurate numerical approximation for the fractional diffusion equation
Journal of Computational Physics
Finite difference approximations for two-sided space-fractional partial differential equations
Applied Numerical Mathematics
A direct O(Nlog2N) finite difference method for fractional diffusion equations
Journal of Computational Physics
High-order finite element methods for time-fractional partial differential equations
Journal of Computational and Applied Mathematics
A banded preconditioner for the two-sided, nonlinear space-fractional diffusion equation
Computers & Mathematics with Applications
Hi-index | 7.29 |
We consider the space fractional advection-dispersion equation, which is obtained from the classical advection-diffusion equation by replacing the spatial derivatives with a generalised derivative of fractional order. We derive a finite volume method that utilises fractionally-shifted Grunwald formulae for the discretisation of the fractional derivative, to numerically solve the equation on a finite domain with homogeneous Dirichlet boundary conditions. We prove that the method is stable and convergent when coupled with an implicit timestepping strategy. Results of numerical experiments are presented that support the theoretical analysis.