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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.

65L20Stability and convergence of numerical methods for ODE
65L05Initial value problems for ODE (numerical methods)
34K40Neutral functional-differential equations
34K28Numerical approximation of solutions of functional-differential equations
34K20Stability theory of functional-differential equations
Full Text: DOI
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