Two step Runge-Kutta-Nyström methods for y″ = f(x, y) and P-stability

Abstract

P-stability is an important requirement in the numerical in- tegration of stiff oscillatory systems, but this desirable feature is not pos sessed by any class of numerical methods for y″ = f(x, y). It is known, for example, that P-stable linear mnultistep methods have maximum or- der two and symmetric one step polynomial collocation methods can't be P-stab1e (Coleman 1992). In this note we show the existence of P- stable methods within a general class of two step Runge-Kutta-Nytröm methods. © Springer-Verlag 2002.