Preservation of oscillations of the Runge Kutta method for equation x0.t/ C ax.t/ C a1x.Tt 􀀀 1U/ D 0

The paper deals with the preservation of oscillations of the Runge Kutta method for equation x0.t/Cax.t/Ca1x.Tt􀀀1U/ D 0. It is proved that oscillations of the analytic solution are preserved by the Runge Kutta method. Special interpolation functions of the numerical solutions are given. It turns out that zeros of the interpolation function of the numerical solution converge to ones of the analytic solution with the same order of accuracy as that of the corresponding Runge Kutta method. Some numerical experiments are presented.