SIAM Journal on Numerical Analysis
The accuracy and stability of an implicit solution method for the fractional diffusion equation
Journal of Computational Physics
Weighted average finite difference methods for fractional diffusion equations
Journal of Computational Physics
Finite difference/spectral approximations for the time-fractional diffusion equation
Journal of Computational Physics
A Fourier method for the fractional diffusion equation describing sub-diffusion
Journal of Computational Physics
Numerical algorithm for the time fractional Fokker-Planck equation
Journal of Computational Physics
SIAM Journal on Numerical Analysis
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
Finite Element Method for the Space and Time Fractional Fokker-Planck Equation
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
A Space-Time Spectral Method for the Time Fractional Diffusion Equation
SIAM Journal on Numerical Analysis
Numerical simulations of 2D fractional subdiffusion problems
Journal of Computational Physics
Explicit and implicit finite difference schemes for fractional Cattaneo equation
Journal of Computational Physics
A compact finite difference scheme for the fractional sub-diffusion equations
Journal of Computational Physics
Numerical Schemes with High Spatial Accuracy for a Variable-Order Anomalous Subdiffusion Equation
SIAM Journal on Scientific Computing
A box-type scheme for fractional sub-diffusion equation with Neumann boundary conditions
Journal of Computational Physics
An implicit RBF meshless approach for time fractional diffusion equations
Computational Mechanics
Compact difference scheme for the fractional sub-diffusion equation with Neumann boundary conditions
Journal of Computational Physics
Alternating direction implicit-Euler method for the two-dimensional fractional evolution equation
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
Orthogonal spline collocation method for the two-dimensional fractional sub-diffusion equation
Journal of Computational Physics
Error Analysis of a Compact ADI Scheme for the 2D Fractional Subdiffusion Equation
Journal of Scientific Computing
Hi-index | 31.46 |
New numerical techniques are presented for the solution of a two-dimensional anomalous sub-diffusion equation with time fractional derivative. In these methods, standard central difference approximation is used for the spatial discretization, and, for the time stepping, two new alternating direction implicit (ADI) schemes based on the L"1 approximation and backward Euler method are considered. The two ADI schemes are constructed by adding two different small terms, which are different from standard ADI methods. The solvability, unconditional stability and H^1 norm convergence are proved. Numerical results are presented to support our theoretical analysis and indicate the efficiency of both methods.