[ont.events] Stepsize Control in Runge-Kutta Algorithms.

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.