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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 ordinary differential equations
65L05 Numerical methods for initial value problems involving ordinary differential equations
34K40 Neutral functional-differential equations
34K28 Numerical approximation of solutions of functional-differential equations (MSC2010)
34K20 Stability theory of functional-differential equations
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