The accuracy and stability of an implicit solution method for the fractional diffusion equation
Journal of Computational Physics
Numerical Solution of Partial Differential Equations: An Introduction
Numerical Solution of Partial Differential Equations: An Introduction
High-order compact exponential finite difference methods for convection-diffusion type problems
Journal of Computational Physics
A Fourier method for the fractional diffusion equation describing sub-diffusion
Journal of Computational Physics
SIAM Journal on Numerical Analysis
Journal of Computational and Applied Mathematics
Compact finite difference method for the fractional diffusion equation
Journal of Computational Physics
A fully discrete difference scheme for a diffusion-wave system
Applied Numerical Mathematics
A compact finite difference scheme for the fractional sub-diffusion equations
Journal of Computational Physics
A high-order exponential scheme for solving 1D unsteady convection-diffusion equations
Journal of Computational and Applied Mathematics
Alternating direction implicit schemes for the two-dimensional fractional sub-diffusion equation
Journal of Computational Physics
Compact alternating direction implicit method for two-dimensional time fractional diffusion equation
Journal of Computational Physics
Hi-index | 7.29 |
A high-order compact exponential finite difference scheme for solving the fractional convection-diffusion equation is considered in this paper. The convection and diffusion terms are approximated by a compact exponential finite difference scheme, with a high-order approximation for the Caputo time derivative. For this fully discrete implicit scheme, the local truncation error is analyzed and the Fourier method is used to discuss the stability. The error estimate is given by the discrete energy method. Numerical results are provided to verify the accuracy and efficiency of the proposed algorithm.