Stability Properties of a Discretized Neutral Delay Differential Equation

[1] BELLEN, A.-ZENNARO, M.: Numerical Methods for Delay Differential Equations, in: Numer. Math. Sci. Comput., Oxford University Press, Oxford, 2003.10.1093/acprof:oso/9780198506546.001.0001Search in Google Scholar

[2] ČERMÁK, J.-JÁNSKÝ, J.-KUNDRÁT, P.: On necessary and sufficient conditionsfor the asymptotic stability of higher order linear difference equations, J. Difference Equ. Appl. 18 (2012), 1781-1800.10.1080/10236198.2011.595406Search in Google Scholar

[3] ELAYDI, S.: An Introduction to Difference Equations. Springer, New York, 2005.Search in Google Scholar

[4] FREEDMAN, H. I.-KUANG, Y.: Stability switches in linear scalar neutral delay equation, Funkcial. Ekvac. 34 (1991), 187-209.Search in Google Scholar

[5] GUGLIELMI, N.: Delay dependent stability regions of Θ-methods for delay differentialequations, IMA J. Numer. Anal. 18 (1998), 399-418.10.1093/imanum/18.3.399Search in Google Scholar

[6] HRABALOVÁ, J.: On stability intervals of Euler methods for a delay differential equation, in: Proc. of APLIMAT-11th Internat. Conf. on Appl. Math. (M. Kováčová, ed.), 2012, Bratislava, STU Bratislava, pp. 153-160.Search in Google Scholar

[7] KOLMANOVSKII, V.-MYSHKIS, A.: Introduction to the Theory and Applicationsof Functional Differential Equations. Kluwer, Dordrecht, 1999.10.1007/978-94-017-1965-0Search in Google Scholar

[8] KUNDRÁT, P.: A note on asymptotic estimate for difference equation with several proportionaldelays, Tatra Mt. Math. Publ. 43 (2009), 109-114.Search in Google Scholar

[9] LEVIN, S. A-MAY, R.: A note on difference delay equations, Theor. Popul. Biol. 9 (1976), 178-187.10.1016/0040-5809(76)90043-5Search in Google Scholar