Compact Alternating Direction Implicit Scheme for Integro-Differential Equations of Parabolic Type

Abstract

In this paper, we present a fast and efficient numerical method to solve a class of parabolic integro-differential equations with weakly singular kernels, compact difference approach for spatial discretization and alternating direction implicit method in time, combined with second-order fractional quadrature rule suggested by Lubich approximating the integral term. The $$L^2$$ stability and convergence are derived. Two numerical examples with known exact solution are given to support the theoretical results.