On Global Error Estimation and Control for ODEs and Parabolic PDEs

Decanato - Facoltà di scienze informatiche

Data d'inizio: 6 Ottobre 2010

Data di fine: 7 Ottobre 2010

SPEAKER: Jens Lang, Darmstadt University of Technology, Germany
DATE: Wednesday, October 6th 2010
PLACE: USI Università della Svizzera italiana, room A13, Red Building (Via G. Buffi 13)
TIME: 10.00

In this talk I will report on some joint activities with Jan Verwer (Center for Mathematics and Computer Science, Amsterdam) and Kristian Debrabant (TU Darmstadt) regarding efficiency and reliability questions for initial value problems. First, systems of ODEs are considered. Existing popular codes focus on efficiency by adaptively optimizing time grids in accordance to local error control. The reliability question, that is, how large are the global errors, has received much less attention. We have implemented classical global error estimation based on the first variational equation, and global error control, for which we have used the property of tolerance proportionality. We have found, using the Runge-Kutta-Rosenbrock method ROS3P as example integrator, that the classical approach is remarkably reliable. For parabolic PDEs, the ODE approach is combined with estimates for the spatial truncation errors based on Richardson extrapolation. Numerical examples are used to illustrate the reliability of the estimation and control strategies.

Studies of mathematics, University of Halle-Wittenberg 
1981-1986 PhD (Halle Wittenberg)
1988 researcher at Zuse Institut Berlin
1990 - 2001 Full Professor, University of Darmstadt, (chair for numerics of PDEs)
Jens Lang is also one of the directors of the research center "Computational Engineering", principal investigator in two DFG-funded excellence-initiatives, i.e in the graduate school of Computational Engineering and in the excellence cluster "Smart Interfaces"

HOST: Prof. Rolf Krause