High-order P-stable multistep methods

摘要

Recently numerical integration of the special IVP y″ = f(t, y) whose solutions are of periodic type have been considered of great interest. P-stability is the appropriate requirement for numerical methods integrating periodic problems. As established by Lambert and Watson (1976) a P-stable linear multistep method has order no greater than two. In this paper, two-step multi-stage linear methods are proposed for numerical integration of periodic problems, and P-stable methods of this type (obtained in a simple form) up to order eight are shown. Finally, those methods are successfully tested.