#
Variable Step Rosenbrock Algorithm
for Transient Analysis of Damped Structures

Robert Piché and Paavo Nevalainen

Department of Mathematics

Tampere University of Technology
Conference on Numerical Methods and
Computational Mechanics in Science and Engineering,
July 15--19, 1996, Miskolc, Hungary.

## Abstract

A Rosenbrock algorithm with varying
time step is adapted for
transient analysis of damped second-order
differential equations.
The time step adjustment is based on an embedded local
truncation error estimation formula.
An interpolation formula can be used for intermediate output.
The stepping formula is L-stable
and the error estimation formula is bounded
for large time steps.
The Rosenbrock algorithm is compared to the Thomas-Gladwell
STEP34 algorithm, which is found to be
only conditionally stable.
Numerical results are given for two linear examples:
a stiff linear two degree of freedom system
and a nonproportionally damped plate.
Postscript file (276K)