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.
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