Computers & Mathematics with Applications
Computers & Mathematics with Applications
Alternating direction implicit schemes for the two-dimensional fractional sub-diffusion equation
Journal of Computational Physics
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
Least-Squares Spectral Method for the solution of a fractional advection-dispersion equation
Journal of Computational Physics
Compact difference scheme for the fractional sub-diffusion equation with Neumann boundary conditions
Journal of Computational Physics
Journal of Computational Physics
Alternating direction implicit-Euler method for the two-dimensional fractional evolution equation
Journal of Computational Physics
Journal of Computational Physics
A radial basis functions method for fractional diffusion equations
Journal of Computational Physics
Journal of Scientific Computing
A banded preconditioner for the two-sided, nonlinear space-fractional diffusion equation
Computers & Mathematics with Applications
Convergence analysis of moving finite element methods for space fractional differential equations
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Orthogonal spline collocation method for the two-dimensional fractional sub-diffusion equation
Journal of Computational Physics
Stable multi-domain spectral penalty methods for fractional partial differential equations
Journal of Computational Physics
Exponentially accurate spectral and spectral element methods for fractional ODEs
Journal of Computational Physics
Two finite difference schemes for time fractional diffusion-wave equation
Numerical Algorithms
Hi-index | 0.05 |
In this paper, we consider the numerical solution of the time fractional diffusion equation. Essentially, the time fractional diffusion equation differs from the standard diffusion equation in the time derivative term. In the former case, the first-order time derivative is replaced by a fractional derivative, making the problem global in time. We propose a spectral method in both temporal and spatial discretizations for this equation. The convergence of the method is proven by providing a priori error estimate. Numerical tests are carried out to confirm the theoretical results. Thanks to the spectral accuracy in both space and time of the proposed method, the storage requirement due to the “global time dependence” can be considerably relaxed, and therefore calculation of the long-time solution becomes possible.