Discretized fractional calculus
SIAM Journal on Mathematical Analysis
A difference scheme for a nonlinear partial integrodifferential equation
SIAM Journal on Numerical Analysis
A finite difference scheme for partial integro-differential equations with a weakly singular kernel
Applied Numerical Mathematics
Applied Mathematics and Computation
Journal of Computational Physics
Finite difference/spectral approximations for the time-fractional diffusion equation
Journal of Computational Physics
SIAM Journal on Numerical Analysis
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
A compact finite difference scheme for the fractional sub-diffusion equations
Journal of Computational Physics
A box-type scheme for fractional sub-diffusion equation with Neumann boundary conditions
Journal of Computational Physics
Alternating direction implicit schemes for the two-dimensional fractional sub-diffusion equation
Journal of Computational Physics
Hi-index | 31.45 |
In this paper, we present a fast and efficient numerical method to solve a two-dimensional fractional evolution equation on a finite domain. This numerical method combines the alternating direction implicit (ADI) approach with the second-order difference quotient in space, the backward Euler in time and order one convolution quadrature approximating the integral term. By using the discrete energy method, we prove that the ADI scheme is unconditionally stable and the numerical solution converges to the exact one with order O(k+h"x^2+h"y^2), where k is the temporal grid size and h"x,h"y are spatial grid sizes in the x and y directions, respectively. Two numerical examples with known exact solution are also presented, and the behavior of the error is analyzed to verify the order of convergence of the ADI-Euler method.