An accurate second-order ADI scheme for three-dimensional tempered evolution problems arising in heat conduction with memory

Abstract

An alternating direction implicit (ADI) scheme is proposed to study the numerical solution of a three-dimensional integrodifferential equation (IDE) with multi-term tempered singular kernels. Firstly, we employ the Crank-Nicolson method and the product integral (PI) rule on a uniform grid to approximate the temporal derivative and the multi-term tempered-type integral terms, thus establishing a second-order temporal discrete scheme. Then, a second-order finite difference method is used for spatial discretization and combined with the ADI technique to improve computational efficiency. Based on regularity conditions, the stability and convergence analysis of the ADI scheme is given by the energy argument. Finally, numerical examples confirm the results of the theoretical analysis and show that the method is effective.