A new `fifth' order method for solving ordinary differential equations
by
Nicolette Moir
Department of Mathematics, The University of Auckland

Although the traditional numerical methods, Runge-Kutta and Linear Multi-step, are very effective for solving ordinary differential equations, they each have some disadvantages. General Linear Methods are a new type of method which combine the multi-stage nature of the Runge-Kutta methods with the multi-value nature of linear multi-step methods. It is possible to retain the good properties of both classes of methods and at the same time to alleviate the bad ones. A special type of General Linear Method, known as an Almost Runge Kutta method, will be presented. The special design of these methods guarantees that they have the same simple stability properties as Runge-Kutta methods. Special attention with be given to a recently discovered fourth order method which, when implemented in the right way, can be treated as fifth order.

Date received: October 9, 2001