Stability of the Euler-Maclaurin methods for neutral differential equations with piecewise continuous arguments (Q884612)

This paper deals with the stability analysis of the Euler-Maclaurin methods for neutral differential equations with piecewise continuous arguments \(u'(t)=au(t)+\sum^N_{i=0}a_iu^{(i)}([t])\). 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.