A1 Refereed original research article in a scientific journal
Variable step Rosenbrock algorithm for transient response of damped structures
Authors: Robert Piché, Paavo Nevalainen
Publisher: SAGE publoicatins
Publishing place: Newbury Park, California
Publication year: 1999
Volume: 358
First page : 191
Last page: 198
Web address : https://www.researchgate.net/publication/245387120_Variable_step_Rosenbrock_algorithm_for_transient_response_of_damped_structures#fullTextFileContent
Self-archived copy’s web address: https://journals.sagepub.com/doi/abs/10.1243/0954406991522266
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 with 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 non-proportionally damped plate.
