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