Oscillations analysis of numerical solutions for neutral delay differential equations

In this paper, we will study oscillations of numerical solutions for the neutral delay differential equation [image omitted] where p∈ and p≠0, τ, q∈(0,+∞), σ≥0. Conditions under which numerical solutions of the above differential equation are oscillatory are obtained. The condition that leads to oscillations of the linear θ-method is also given. To verify our results, we give numerical experiments.