On the stability of a two-step method for solving periodic IVPs

In Appl. Math. Math. 138 (2003) 435, we presented a nonlinear explicit method for solving periodic initial value problems, which is P-stable in the sense of Lambert and Watson. However, it is not sufficient to investigate the stability behavior of the method based on the scalar test equation y″ = −λy. After introducing a new test system and extending the definitions of the interval of periodicity and the phase-lag, we discuss the stability property and the phase-lag of the method in this note.