An ADI difference scheme based on fractional trapezoidal rule for fractional integro-differential equation with a weakly singular kernel.

Abstract In this paper, we propose a fast and efficient numerical method to solve the two-dimensional integro-differential equation with a weakly singular kernel. The numerical method are considered by finite difference approach for spatial discretization and alternating direction implicit (ADI) method in time, combined with the second-order fractional quadrature convolution rule introduced by Lubich and the classical L 1 approximation for Caputo fractional derivative. The detailed analysis shows that the proposed scheme is unconditionally stable and convergent with the convergence order O (τ min { 1 + α , 2 − α } + h 1 2 + h 2 2). Some numerical results are also given to confirm our theoretical prediction. [ABSTRACT FROM AUTHOR]