Abstract
When solving stiff mechanical systems, implicit time integrators overestimate the error and tend to use small stepsizes due to the order reduction phenomenon. This article introduces an algorithm for the detection of stiff components that allows automatic scaling of the stepsize h in the error estimation. It is based on an investigation of the local error and applies existing embedded formulas of implicit Runge–Kutta methods. Thus, implementation and calculation effort are low. Three examples are integrated with the code RADAU5, a linear DAE in two different formulations and a slider crank mechanism.
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Schaub, M., Simeon, B. Automatic h-Scaling for the Efficient Time Integration of Stiff Mechanical Systems. Multibody System Dynamics 8, 327–343 (2002). https://doi.org/10.1023/A:1020973630828
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DOI: https://doi.org/10.1023/A:1020973630828