Oscillation analysis of numerical solution in the θ-methods for equation x′(t) + ax(t) + a1x([t − 1]) = 0

The paper deals with the oscillation analysis of numerical solution in the θ-methods for equation x′(t) + ax(t) + a1x([t − 1]) = 0. The conditions of the oscillation for the θ-method are obtained. It is proved that the oscillation of the analytic solution is preserved by the θ  -method. It turns out that the zeros of the linear interpolation function of the numerical solution can converge to the zeros of the analytic solution with the order of accuracy 1 θ≠12 and 2 θ=12. Some numerical experiments are given.