Summary
In this article, we study a class of numerical ODE schemes that use a time filtering strategy and operate in two time scales. The algorithms follow the framework of the heterogeneous multiscale methods (HMM) [1]. We apply the methods to compute the averaged path of the inverted pendulum under a highly oscillatory vertical forcing on the pivot. The averaged equation for related problems has been studied analytically in [9]. We prove and show numerically that the proposed methods approximate the averaged equation and thus compute the average path of the inverted pendulum.
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Sharp, R., Tsai, YH., Engquist, B. (2005). Multiple Time Scale Numerical Methods for the Inverted Pendulum Problem. In: Engquist, B., Runborg, O., Lötstedt, P. (eds) Multiscale Methods in Science and Engineering. Lecture Notes in Computational Science and Engineering, vol 44. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-26444-2_13
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DOI: https://doi.org/10.1007/3-540-26444-2_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-25335-8
Online ISBN: 978-3-540-26444-6
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