## 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)

### Keywords:

neutral delay differential equations; numerical method
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### References:

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