An L-stable Rosenbrock Method for Step-by-Step Time Integration in Structural Dynamics

Robert Piché
Department of Mathematics
Tampere University of Technology

Computer Methods in Applied Mechanics and Engineering, 126 (1995) 343-354.


A single-step two-stage L-stable Rosenbrock method is given in a form suitable for step-by-step integration of linear and nonlinear structural dynamics problems. The method has second-order accuracy and is a true single-step method, in that it does not require initial values of acceleration. For each time step, the method requires a single formation of the tangential stiffness matrix, a single LU decomposition, and two linear system substitutions, but does not require iteration. Analysis and numerical examples are used to show the good stability and accuracy properties of the method and the importance of L-stability when integrating numerically stiff problems in structural dynamics.