Dynamic Behavior of Euler-Maclaurin Methods for Differential Equations with Piecewise Constant Arguments of Advanced and Retarded Type

Abstract

The paper deals with three dynamic properties of the numerical solution for differential equations with piecewise constant arguments of advanced and retarded type: oscillation, stability and convergence. The Euler-Maclaurin methods are used to discretize the equations. According to the characteristic theory of the difference equation, the oscillation and stability conditions of the numerical solution are obtained. It is proved that the convergence order of numerical method is 2n+2. Furthermore, the relationship between stability and oscillation is discussed for analytic solution and numerical solution, respectively. Finally, several numerical examples confirm the corresponding conclusions.