Nonlinear stability of discontinuous Galerkin methods for delay differential equations

The present paper is devoted to a study of nonlinear stability of discontinuous Galerkin methods for delay differential equations. Some concepts, such as global and analogously asymptotical stability are introduced. We derive that discontinuous Galerkin methods lead to global and analogously asymptotical stability for delay differential equations. And these nonlinear stability properties reveal to the reader the relation between the perturbations of the numerical solution and that of the initial value or the systems.