Department of Mathematics,
Arizona State University
Thursday,
January 27, 2000, 12:30 p.m. in GWC Room 604
Jim Verner
Department of Mathematics and Statistics, Queen's University, Kingston, Ontario, Canada
Ramifications of the Derivation of Explicit Runge-Kutta Methods
Abstract
The derivation of order conditions for discrete variable methods
which are used to solve initial value problems in ordinary
differential equations has been studied by many authors.
In particular, the study and application of rooted trees
in this process by J.C. Butcher has simplfied this process.
Fewer authors have been successful in solving the order
conditions for moderate to high order methods althought
Butcher has developed a number of elegant approaches for
this purpose. By adding other techniques to these, I have
been able to classify and derive parametric families of
high order explicit Runge--Kutta methods and pairs.
These techniques have been generalized to obtain continuous
explicit Runge--Kutta methods, Bel'tyukov methods for
Volterra integral equations and formulas for estimating
global error in explicit Runge-Kutta methods. In this talk
I shall survey some of these approaches, and indicate an
advantage of interpreting the Dormand-Prince approach to
global error estimation as a general linear method.
For further information please contact:
mittelmann@asu.edu