MAXIMUM ERROR ESTIMATES OF DISCONTINUOUS GALERKIN METHODS FOR SOLVING NEUTRAL DELAY DIFFERENTIAL EQUATIONS

The exact solution to a neutral delay differential equation is generally non-smooth. Some possible loss of accuracy is usually found if certain high-order numerical methods are applied. The discontinuous Galerkin (DG) methods are introduced to numerically solve neutral delay differential equations so as to handle the difficulties. Maximum error estimates of the numerical method is investigated. Theoretical results indicate that the ${p}$-degree DG approximate solution has an accuracy of ${p}$-th order. Numerical experiments are presented to confirm the effectiveness and performance of the DG methods.