Faithful Forever
by
John Butcher
The University of Auckland

In the 1939 animated film adaptation of Gulliver's Travels, the two rival kingdom's of Lilliput and Blefuscu are on track to be united through a royal marriage but they have their own national songs. Fortunately, the words of ``Faithful'' and ``Forever" can be juxtaposed to make a new song which everyone likes.

In the numerical solution of evolutionary problems, we want computed results to be faithful to the trajectories they are approximating. We also want the behaviour of the approximation to be qualitatively (or geometrically) correct for a very long time --- essentially forever.

This talk will consider how to combine ``Faithful'' and ``Forever'' to obtain numerical approximations which are successful both quantitatively and qualitatively, so that everyone should like them.

Date received: December 22, 2009