B-Stability Of Time-Integration Schemes and the Softening Spring Example

Robert Piché
Department of Mathematics
Tampere University of Technology

Proc. 8th Nordic Seminar on Computational Mechanics, Gotheborg, Sweden, Nov. 16-18, 1995.


The concepts of B-stability and G-stability of numerical time-integration schemes are discussed in relation to nonlinear structural dynamics problems. The trapezoid method is not B-stable but the closely related midpoint method is B-stable. There is an L-stable two-stage Runge-Kutta method that is B-stable. Park's method is G-stable. The softening spring example is used to illustrate the stability properties.