Study of the backward difference and local discontinuous Galerkin (LDG) methods for solving fourth-order partial integro-differential equations (PIDEs) with memory terms: Stability analysis

Abstract

In the current paper, we use backward difference and local discontinuous Galerkin (BD-LDG) methods for temporal and spatial discretization of fourth-order partial integro-differential equations (PIDEs) with memory terms containing weakly singular kernels. This work provides a stability analysis of the proposed method, and at the end, by presenting some numerical experiments, we demonstrate the stability of the resulting scheme and show numerically that the optimal convergence rate is O(hk+1) in the discrete L2 norm.