Discretized fractional calculus
SIAM Journal on Mathematical Analysis
Applied Mathematics and Computation
Numerical methods for the solution of partial differential equations of fractional order
Journal of Computational Physics
Finite difference approximations for fractional advection-dispersion flow equations
Journal of Computational and Applied Mathematics
SIAM Journal on Numerical Analysis
The accuracy and stability of an implicit solution method for the fractional diffusion equation
Journal of Computational Physics
Finite difference methods for two-dimensional fractional dispersion equation
Journal of Computational Physics
Weighted average finite difference methods for fractional diffusion equations
Journal of Computational Physics
A second-order accurate numerical method for the two-dimensional fractional diffusion equation
Journal of Computational Physics
A Fourier method for the fractional diffusion equation describing sub-diffusion
Journal of Computational Physics
SIAM Journal on Numerical Analysis
Matrix approach to discrete fractional calculus II: Partial fractional differential equations
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Compact finite difference method for the fractional diffusion equation
Journal of Computational Physics
Numerical simulations of 2D fractional subdiffusion problems
Journal of Computational Physics
A direct O(Nlog2N) finite difference method for fractional diffusion equations
Journal of Computational Physics
High order compact Alternating Direction Implicit method for the generalized sine-Gordon equation
Journal of Computational and Applied Mathematics
A compact finite difference scheme for the fractional sub-diffusion equations
Journal of Computational Physics
Journal of Computational Physics
Compact difference scheme for the fractional sub-diffusion equation with Neumann boundary conditions
Journal of Computational Physics
A radial basis functions method for fractional diffusion equations
Journal of Computational Physics
Journal of Scientific Computing
A high-order compact exponential scheme for the fractional convection-diffusion equation
Journal of Computational and Applied Mathematics
Operator splitting ADI schemes for pseudo-time coupled nonlinear solvation simulations
Journal of Computational Physics
Journal of Computational Physics
Error Analysis of a Compact ADI Scheme for the 2D Fractional Subdiffusion Equation
Journal of Scientific Computing
Hi-index | 31.47 |
High-order compact finite difference scheme with operator splitting technique for solving two-dimensional time fractional diffusion equation is considered in this paper. A Grunwald-Letnikov approximation is used for the Riemann-Liouville time derivative, and the second order spatial derivatives are approximated by the compact finite differences to obtain a fully discrete implicit scheme. Alternating direction implicit (ADI) method is used to split the original problem into two separate one-dimensional problems. The local truncation error is analyzed and the stability is discussed by the Fourier method. The proposed scheme is suitable when the order of the time fractional derivative @c lies in the interval 12,1. A correction term is added to maintain high accuracy when @c@?0,12. Numerical results are provided to verify the accuracy and efficiency of the proposed algorithm.