Numerical oscillation of neutral logistic delay differential equation

• The equation is transformed by an invariant oscillation transformation.
• Some conditions under which the numerical solution oscillates are obtained.
• We consider the asymptotic property of non-oscillatory numerical solution.

This paper mainly deals with the oscillation of numerical solution for the neutral logistic delay differential equation. Applying the θθ-methods to the simplified type of the original equation which is got through an invariant oscillation transformation. It is proven that every non-oscillatory numerical solution tends to the steady state of the model. Moreover, some conditions under which the numerical solution oscillates are obtained. Finally, to demonstrate our theoretical results, some numerical examples are adopted.