Local discontinuous Galerkin methods for the time tempered fractional diffusion equation

摘要

In this article, we consider high order discrete schemes for solving the time tempered fractional diffusion equation. We present a semi-discrete scheme by using the local discontinuous Galerkin (LDG) discretization in the spatial variable. We prove that the semi-discrete scheme is unconditionally stable in L2 norm and convergence with optimal convergence rate O(hk+1), where h is the spatial step size. We develop a class of fully discrete LDG schemes by combining the weighted and shifted Lubich difference operators with respect to the time variable, and establish the error estimates. Finally, numerical experiments are presented to verify the theoretical results.