In this paper, we derive a class of new hybrid linear multistep methods (HLMMs) for the numerical solution of second order initial value problems (IVPs) in ordinary differential equations (ODEs). The proposed schemes possess p-stability properties which show that they are capable of handling IVPs that are periodic in nature. Some numerical experiments are performed to show the accuracy of the new algorithms.

p-stability, hybrids, LMMs, Padé approximation, symmetric, interval of periodicity.