Stability of the Euler-Maclaurin methods for neutral differential equations with piecewise continuous arguments

This paper deals with the stability analysis of the Euler-Maclaurin methods for neutral differential equations with piecewise continuous arguments u′(t)=au(t)+∑i=0Naiu(i)([t]). The stability regions of the Euler-Maclaurin methods are determined. The conditions under which the analytic stability region is contained in the numerical stability region are obtained and some numerical experiments are given.