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.