Lv, W. J.; Yang, Z. W.; Liu, M. Z. Stability of the Euler-Maclaurin methods for neutral differential equations with piecewise continuous arguments. (English) Zbl 1175.65088 Appl. Math. Comput. 186, No. 2, 1480-1487 (2007). 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. Cited in 12 Documents 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 Keywords:delay differential equation; piecewise continuous arguments; asymptotic stability; numerical asymptotic stability; Euler-Maclaurin methods; neutral differential equations; numerical experiments PDFBibTeX XMLCite \textit{W. J. Lv} et al., Appl. Math. Comput. 186, No. 2, 1480--1487 (2007; Zbl 1175.65088) Full Text: DOI References: [1] Bainov, D.; Kostandinov, T.; Petrov, V., Oscillatory and asymptotic properties of nonlinear first order neutral differential equations with piecewise constant argument, J. Math. Anal. Appl., 194, 621-639 (1995) · Zbl 0842.34070 [2] Busenberg, S.; Cooke, K. L., Models of vertically transmitted diseases with sequential-continuous dynamics, (Lakshmikantham, V., Nonlinear Phenomena in Mathematical Sciences (1982), Academic Press: Academic Press New York), 179-187 · Zbl 0512.92018 [3] Dahlquist, G.; Björck, Å., Numerical Methods, Prentice-Hall Ser. Automat. Comput (1974), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ, (Translated from the Swedish by Ned Anderson) [4] Gopalsamy, K., Stability and Oscillation in Delay Differential Equations of Population Dynamics (1992), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht · Zbl 0752.34039 [5] Györi, I.; Ladas, G., Oscillation Theory of Delay Differential Equations with Applications (1991), Oxford University Press: Oxford University Press Oxford · Zbl 0780.34048 [6] Stoer, J.; Bulirsh, R., Introduction to Numerical Analysis, Texts Appl. Math. (1993), Springer: Springer New York, (Translated from the German by R. Bartels, W. Gantschi, C. Witzgall) [7] Wiener, J., Generalized Solutions of Functional Differential Equations (1993), World Scientific: World Scientific Singapore · Zbl 0874.34054 [8] Yuan, R., Pseudo-almost periodic solutions of second-order neutral delay differential equations with piecewise constant argument, Nonlinear Anal., 41, 871-890 (2000) · Zbl 1024.34068 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.