An alternating direction implicit orthogonal spline collocation method for the two dimensional multi-term time fractional integro-differential equation

Abstract In this paper, a new numerical approximation is discussed for the two dimensional multi-term time fractional integro-differential equation. The proposed technique is based on the high order orthogonal spline collocation (OSC) method for the spatial discretization, the classical L1 approximation for the Caputo fractional derivative, and an alternating direction implicit (ADI) method in time, combined with the second order fractional quadrature rule proposed by Lubich to approximate the integral term. Detailed analysis for the optimal error estimate of the proposed scheme is rigorously discussed. Numerical results are listed to support the theoretical analysis.