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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.

MSC:

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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