A class of two-step P-stable methods for the accurate integration of second order periodic initial value problems

In this paper we consider a two parameter family of two-step methods for the accurate numerical integration of second order periodic initial value problems. By applying the methods to the test equation y″ + λ²y = 0, we determine the parameters α, β so that the phase-lag (frequency distortion) of the method is minimal. The resulting method is a P-stable method with a minimal phase-lag λ⁶h⁶/42000. The superiority of the method over the other P-stable methods is illustrated by a comparative study of the phase-lag errors and by illustrating with a numerical example.