Runge--Kutta--Nyström methods with maximized stability domain in structural dynamics

Authors:
Christoph Lunk;Bernd Simeon
Affiliations:
Technische Universität München, Zentrum Mathematik, Boltzmannstrasse 3, D-85747 Garching, Germany;Technische Universität München, Zentrum Mathematik, Boltzmannstrasse 3, D-85747 Garching, Germany
Venue:
Applied Numerical Mathematics
Year:
2005

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Abstract

Structural dynamics applications feature a particular type of second order stiff equations, often in combination with low smoothness of the right side, large dimension and non-linear forcing terms. As alternative to implicit schemes, explicit Runge-Kutta-Nystrom methods are analysed, with focus on low order and maximized stability domain since spurious high frequency oscillations need not be resolved. It turns out that it is possible to construct methods with a stability domain that stretches up to h@w=2s on the imaginary axis where h is the stepsize, @w the largest frequency in the system, and s the stage number. Simulation examples generated by FEMLAB show that the methods are competitive.