A second-order finite difference scheme for nonlinear tempered fractional integrodifferential equations in three dimensions.

In this paper, we provide a numerical solution for the nonlinear tempered fractional integrodifferential equation in three dimensions. We use the trapezoidal convolution rule with backward differences (BDF2) for temporal discretization, and develop an alternating direction implicit difference scheme for spatial discretization. A novel fast approximation is applied to tackle the nonlinear term. The stability and convergence analysis of the numerical scheme are analyzed. Furthermore, some numerical experiments are provided to confirm the theoretical results. [ABSTRACT FROM AUTHOR]