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Stability of the Euler-Maclaurin methods for neutral differential equations with piecewise continuous arguments. (English) Zbl 1175.65088
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.

##### MSC:
 65L20 Stability and convergence of numerical methods for ODE 65L05 Initial value problems for ODE (numerical methods) 34K40 Neutral functional-differential equations 34K28 Numerical approximation of solutions of functional-differential equations 34K20 Stability theory of functional-differential equations
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##### References:
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