Abstract
For the single-step time-integration algorithm formulated by Zienkiewicz et al., a weight function of the form tr is posed. The weight parameters θ are found through a simple formula for a range of values r. These are used to integrate three numerical formulations of the non-linear dynamics equation for a planar pendulum. Comparisons with existing integration methods show that, for r non-positive, the r-methods are accurate, stable and very competitive. Results are dependent both upon r and the formulation. Useful ranges for r are discussed.
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