3rd Brig Workshop on Dissipativity in Systems and Control

Long time convergence of Runge-Kutta methods for dissipative ordinary differential equations on infinite time intervals

May 28, 2026, 10:30 AM

35m

FernUni Schweiz - UniDistance Suisse

Contributed talk

Speaker

Prof. Chengming Huang (School of Mathematics and Statistics, Huazhong University of Science and Technology)

Description

In this talk, we are concerned with the numerical solution of stiff ordinary differential equations by Runge-Kutta methods. A B-convergence result on infinite time intervals is provided for algebraically stable methods applied to strictly dissipative systems. As an application of this result, the $s$-stage Radau IIA methods are proved to be B-convergent of order $s$ on infinite time intervals, and the $s$-stage Radau IA and Lobatto IIIC methods are B-convergent of order $s-1$ on infinite time intervals. Compared to Theorem 15.3 in the monograph [1] by Hairer and Wanner, the error bounds obtained here are independent of the length of the integration interval and are applicable to infinite time intervals.

[1] E. Hairer and G. Wanner, Solving ordinary differential equations. II. Stiff and differential-algebraic problems. Second edition. Springer Series in Computational Mathematics, 14. Springer-Verlag, Berlin, 1996.