Oscillations analysis of numerical solutions for neutral delay differential equations. (English) Zbl 1230.34066

Summary: We study oscillations of numerical solutions for the neutral delay differential equation \[ \frac{d}{dt}[y(t) + py(t-\tau )] + qy(t-\sigma)=0, \] where \(p \in \mathbb R\) and \(p\neq 0\), \(\tau , q \in (0,+\infty )\), \(\sigma \geq 0\). Conditions under which numerical solutions of the above differential equation are oscillatory are obtained. A condition that leads to oscillations of the linear \(\theta \)-method is also given. To verify our results, we give numerical experiments.


34K40 Neutral functional-differential equations
34K06 Linear functional-differential equations
34K11 Oscillation theory of functional-differential equations
34K28 Numerical approximation of solutions of functional-differential equations (MSC2010)
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[1] DOI: 10.1016/0022-247X(67)90191-6 · Zbl 0155.47302 · doi:10.1016/0022-247X(67)90191-6
[2] DOI: 10.1109/81.739268 · Zbl 0952.94015 · doi:10.1109/81.739268
[3] Driver R. D., Methods Appl. 8 pp 155– (1984)
[4] Gopalsamy K., Stability and Oscillations in Population Dynamics (1992) · Zbl 0752.34039
[5] Györi I., Oscillation Theory of Delay Differential Equations with Applications (1991) · Zbl 0780.34048
[6] Hale J. K., Theory of Functional Differential Equations (1977) · Zbl 0352.34001
[7] DOI: 10.1016/j.amc.2006.07.119 · Zbl 1118.65080 · doi:10.1016/j.amc.2006.07.119
[8] DOI: 10.1016/j.camwa.2009.07.030 · Zbl 1189.65143 · doi:10.1016/j.camwa.2009.07.030
[9] DOI: 10.1016/S0096-3003(03)00300-X · Zbl 1045.34038 · doi:10.1016/S0096-3003(03)00300-X
[10] Snow, W. 1965. ”Existence uniqueness and stability for nonlinear differential-difference equations in the neutral case”. New York: Courant Institute of Mathematical Sciences, New York University. Report No. IMM NYU 328 Available athttp://www.archive.org/details/existenceuniquen00snow
[11] DOI: 10.1016/j.mcm.2006.11.014 · Zbl 1151.34327 · doi:10.1016/j.mcm.2006.11.014
[12] DOI: 10.1016/j.chaos.2005.12.020 · Zbl 1146.34330 · doi:10.1016/j.chaos.2005.12.020
[13] DOI: 10.1016/j.amc.2003.12.081 · Zbl 1063.65070 · doi:10.1016/j.amc.2003.12.081
[14] DOI: 10.1016/j.aml.2006.01.003 · Zbl 1190.34079 · doi:10.1016/j.aml.2006.01.003
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