Stiff and non-stiff general linear methods for ordinary differential equations
by
Will Wright
The University of Auckland

A new class of diagonally implicit general linear methods for the application of stiff differential equations, has recently been studied by John Butcher. This class of methods has a property known as `inherent RK stability', which guarantees the stability matrix has a single non-zero eigenvalue. This talk will concentrate on two main points. First it will be shown how to derive explicit methods with the inherent Runge-Kutta stability property suitable for non-stiff problems. The transformation discussed in John's talk, can also be used to find implicit methods with an underlying explicit structure. Secondly it will be shown how it is possible to find a large class of inherently RK stable methods, using what are known as `doubly companion matrices'. It is believed that the process of obtaining a comprehensive scheme of both stiff and non-stiff methods is now complete.

Date received: September 27, 2000