Computational and Applied Math Proseminar

Department of Mathematics and Statistics, Arizona State University

Tuesday, September 14, 2004, 12:15 p.m. in GWC Room 110

Karel in 't Hout

Department of Mathematics&Statistics

Stability of adaptations of Runge-Kutta methods to stiff delay differential equations

Abstract This talk deals with the numerical solution of stiff initial value problems for delay differential equations. Initial value problems of this kind arise frequently in for example immunology. For the numerical solution of these problems, we consider the adaptation of the well-known class of Runge-Kutta methods.

In order to obtain the adaptation we shall deal in this talk with the interpolation procedure that was recently formulated by Guglielmi and Hairer (2001). For a given Runge-Kutta process and a time point t, this interpolation procedure computes an approximation to the exact solution at t by evaluating the polynomial that (only) passes through the stage values from the time step corresponding to t.

The important question arises whether the above interpolation procedure leads to an adaptation of the class of Runge-Kutta methods to stiff delay differential equations that has favorable stability properties. Up to now, this question seems to be completely open in the literature, and in this talk we will present several (numerical and theoretical) results. In particular we shall consider here the adaptation of the popular family of Radau IIA methods.

For further information please contact: mittelmann@asu.edu