Stability analysis of discontinuous Galerkin method for stiff Volterra functional differential equations

Abstract

This paper concerns the nonlinear stability properties of discontinuous Galerkin (DG) method for stiff Volterra functional differential equations (VFDEs). We derive that the DG method leads to global and analogously asymptotical stability for VFDEs, and it is shown that the perturbations of the numerical solution are controlled by the initial perturbations. This general results provide unified theoretical treatment for numerical stability analysis of Volterra integro-differential equations (VIDEs) with constant or variable delay, delay differential equations (DDEs), ordinary differential equations (ODEs) and so on. Numerical examples are given to confirm our theoretical results.