High Order Integration of Smooth Dynamical Systems: Theory and Numerical Experiments
Technical research rept.
MARYLAND UNIV COLLEGE PARK INST FOR SYSTEMS RESEARCH
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This paper describes a new class of algorithms for integrating linear second order equations and those containing smooth nonlinearities. The algorithms are based on a combination of ideas from standard Newmark integration methods and extrapolation techniques. For the algorithm to work the underlying Newmark method must be stable second order accurate, and produce asymptotic error expansions for response quantities containing only even ordered terms. It is proved that setting the Newmark parameter Gamma to 12 gives a desirable asymptotic expansion, irrespective of the setting for Beta. Numerical experiments are conducted for two linear and two nonlinear applications.
- Numerical Mathematics