P-stable boundary value methods for second order IVPs

We introduce a family of Linear Multistep Methods used as Boundary Value Methods for the numerical solution of initial value problems for second order ordinary differential equations of special type. The aim is to obtain P-stable methods with arbitrary order of accuracy. This result allows to overcome the order barrier established by Lambert and Watson which limited to p - 2 the maximum order of a P-stable Linear Multistep Method. In addition, an extension of the methods in the Exponential Fitting framework is also considered