A direct O(Nlog2N) finite difference method for fractional diffusion equations
Journal of Computational Physics
A characteristic difference method for the transient fractional convection-diffusion equations
Applied Numerical Mathematics
Alternating direction implicit schemes for the two-dimensional fractional sub-diffusion equation
Journal of Computational Physics
Multigrid method for fractional diffusion equations
Journal of Computational Physics
Finite Elements in Analysis and Design
Error Estimates of Crank-Nicolson-Type Difference Schemes for the Subdiffusion Equation
SIAM Journal on Numerical Analysis
A second order explicit finite difference method for the fractional advection diffusion equation
Computers & Mathematics with Applications
Regularization methods for unknown source in space fractional diffusion equation
Mathematics and Computers in Simulation
Alternating direction implicit-Euler method for the two-dimensional fractional evolution equation
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
Orthogonal spline collocation methods for the subdiffusion equation
Journal of Computational and Applied Mathematics
Orthogonal spline collocation method for the two-dimensional fractional sub-diffusion equation
Journal of Computational Physics
Preconditioned iterative methods for fractional diffusion equation
Journal of Computational Physics
Stable multi-domain spectral penalty methods for fractional partial differential equations
Journal of Computational Physics
Fully discrete local discontinuous Galerkin method for solving the fractional telegraph equation
Calcolo: a quarterly on numerical analysis and theory of computation
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We develop the finite element method for the numerical resolution of the space and time fractional Fokker-Planck equation, which is an effective tool for describing a process with both traps and flights; the time fractional derivative of the equation is used to characterize the traps, and the flights are depicted by the space fractional derivative. The stability and error estimates are rigorously established, and we prove that the convergent order is $O(k^{2-\alpha}+h^\mu)$, where $k$ is the time step size and $h$ the space step size. Numerical computations are presented which demonstrate the effectiveness of the method and confirm the theoretical claims.