Abstract
In this paper, we consider the numerical solutions of the two dimensional fractional evolution equation (integro-differential equation with a weakly singular kernel) with alternating direction implicit (ADI) method. The compact difference approach is used for the spatial discretization, and, for the time stepping, the Crank- Nicolson scheme combined with the second order convolution quadrature approximating the integral term is considered. The unconditional stability and L 2 norm convergence of the scheme are proved rigorously. The convergence order is O ( τ 2 + h x 4 + h y 4), where τ is the temporal grid size and h x , h y are spatial grid sizes in the x and y directions, respectively. Numerical results are presented to support our theoretical analysis.
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