Symmetric multistep methods with zero phase-lag for periodic initial value problems of second order differential equations

We present in this paper two-step and four-step symmetric multistep methods involving a parameter p to solve a special class of initial value problems associated with second order ordinary differential equations in which the first derivative does not appear explicitly. It is shown that the methods have zero phase-lag when p is chosen as 2π times the frequency of the given initial value problem. The periodicity intervals are given in terms of expressions involving the parameter p. As p increases, the periodicity intervals increase and for large p, the methods are almost P-stable.