Multiple time scale numerical methods for the inverted pendulum problem (2004) [1 citations — 1 self]
Download:
by Richard Sharp, Yen-hsi Tsai, Bjorn Engquist
ftp://ftp.math.ucla.edu/pub/camreport/cam04-33.pdf
Add To MetaCart
Abstract:
ABSTRACT. In this article, we study a class of numerical ODE schemes that use 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 the 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. 1.
Citations
| 28 | Long-time-step methods for oscillatory differential equations – García-Archilla, Sanz-Serna, et al. - 1998 |
| 21 | The heterogeneous multiscale method – E, Engquist - 2003 |
| 16 | Multirate linear multistep methods – GEAR, D - 1984 |
| 13 | An efficient numerical method for highly oscillatory ordinary differential equations – Petzold - 1981 |
| 5 | A reversible averaging integrator for multiple time-scale dynamics – Leimkuhler, Reich |
| 4 | Geometric numerical integration, volume 31 – Hairer, Lubich, et al. - 2002 |
| 3 | Automatic methods for highly oscillatory ordinary differential equations – Gear, Gallivan - 1981 |
| 2 | Heterogeneous multiscale methods for stiff ordinary differential equations. 2003. Under review – Engquist, Tsai - 2005 |
| 2 | Geometry and physics of averaging with applications. Phys. D – Levi - 1999 |
| 1 | Heterogeneous multiscle method for phase transitions – Weinan, Li |
