21st Century COE Lectures

Date : May 17 (The) 15:00 - 16:00
Place : Room 115, RIMS
Lecturer: John Butcher
(University of Auckland)
Title : Runge-Kutta methods for ordinary differential equations
Abstract: Runge-Kutta methods are widely used in modern computation. This survey will include a discussion of their order conditions and attempts to construct methods which satisfy these conditions. An outline proof will be given of the main order barrier (fifth order methods require more than 5 stages) and related results will be summarised. This will lead to a the idea of effective order as a means of avoiding some of the consequences of this barrier. For the solution of stiff problems, the use of implicit methods is preferred and some of the important families of implicit Runge-Kutta methods will be introduced.

Research Institute for Mathematical Sciences Department of Mathematics, Kyoto University

Last modified: May 2, 2005