Hybrid methods in Nordsieck Representation
by
Alannah O'Sullivan
The University of Auckland

Hybrid methods are a modification to linear multistep methods, and involve the addition of one or more off-step points. This modification adds a Runge-Kutta flavour to the method which enables the achievable order of the method to exceed Dahlquist's barrier. Originally hybrid methods were formulated in the traditional manner of linear multistep methods; this makes variable stepsize even more complicated than for Adams methods. To overcome this difficulty, we reformulate the method in Nordsieck form. We also discuss such practical considerations as a startup procedure and error estimation. Preliminary testing and comparisons with popular methods show the hybrid method to be promising.

Date received: September 28, 2000