ylfink@water.waterloo.edu (ylfink) (11/12/88)
DEPARTMENT OF COMPUTER SCIENCE
UNIVERSITY OF WATERLOO
SEMINAR ACTIVITIES
SCIENTIFIC COMPUTATION SEMINAR
- Thursday, November 17, 1988
Dr. Desmond Higham, University of Toronto, will speak
on ``Stepsize Control in Runge-Kutta Algorithms''.
TIME: 4:00 PM
ROOM: DC 1304
ABSTRACT
Modern explicit Runge-Kutta (RK) codes for solving
initial value problems employ automatic stepsize
selection procedures. This talk deals with the
behaviour of these procedures on the restricted class
of mildly stiff problems. On such problems it has been
observed that some RK codes behave efficiently by
taking the largest stable stepsize, whilst others
produce an erratic and inefficient stepsize pattern
which oscillates about the stability boundary. By
analysing model problems we obtain a simple criterion,
depending only on the coefficients of the RK formula,
to determine which of the two types of behaviour will
occur. We then show that it is possible to derive high
quality RK formulae which are effective in the presence
of mild stiffness. Finally, we discuss some recent
extensions of this work which allow for the use of a
mixed relative-absolute error measure in the stepsize
selection process. Throughout the talk, numerical
results will be used to illustrate the theory.
The work presented here was performed jointly with
George Hall.