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 methods for two-dimensional fractional dispersion equation
Journal of Computational Physics
Finite difference approximations for two-sided space-fractional partial differential equations
Applied Numerical Mathematics
Least squares finite-element solution of a fractional order two-point boundary value problem
Computers & Mathematics with Applications
A second-order accurate numerical method for the two-dimensional fractional diffusion equation
Journal of Computational Physics
Numerical approximation of Lévy-Feller diffusion equation and its probability interpretation
Journal of Computational and Applied Mathematics
A Fourier method for the fractional diffusion equation describing sub-diffusion
Journal of Computational Physics
Numerical solutions for fractional reaction-diffusion equations
Computers & Mathematics with Applications
Computers & Mathematics with Applications
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Applied Numerical Mathematics
A note on the finite element method for the space-fractional advection diffusion equation
Computers & Mathematics with Applications
An implicit RBF meshless approach for time fractional diffusion equations
Computational Mechanics
Computers & Mathematics with Applications
Journal of Computational Physics
A second order explicit finite difference method for the fractional advection diffusion equation
Computers & Mathematics with Applications
Least-Squares Spectral Method for the solution of a fractional advection-dispersion equation
Journal of Computational Physics
Journal of Scientific Computing
Gauss-Jacobi-type quadrature rules for fractional directional integrals
Computers & Mathematics with Applications
Orthogonal spline collocation method for the two-dimensional fractional sub-diffusion equation
Journal of Computational Physics
Exponentially accurate spectral and spectral element methods for fractional ODEs
Journal of Computational Physics
Journal of Computational Physics
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In this paper, we investigate the numerical approximation of the variational solution to the fractional advection dispersion equation (FADE) on bounded domains in R2. More specifically, we investigate the computational aspects of the Galerkin approximation using continuous piecewise polynomial basis functions on a regular triangulation of the domain. The computational challenges of approximating the solution to fractional differential equations using the finite element method stem from the fact that a fractional differential operator is a non-local operator. Several numerical examples are given which demonstrate approximations to FADEs.