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.

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