How Many Timesteps for a Cycle? Analysis of the Wisdom-Holman Algorithm |
| |
Authors: | Divakar Viswanath |
| |
Institution: | (1) Departments of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA |
| |
Abstract: | The Wisdom-Holman algorithm is an effective method for numerically solving nearly integrable systems. It takes into account the exact solution of the integrable part. If the nearly integrable system is the solar system, for example, the Wisdom-Holman algorithm uses the solution consisting of Keplerian orbits obtained when the interplanetary interactions are ignored. The effectiveness of the algorithm lies in its ability to take long timesteps. We use the Duffing oscillator and Kepler's problem with forcing to deduce how long those timesteps can be. For nearly Keplerian orbits, the timesteps must be at least six per orbital period even when the orbital eccentricity is zero. High eccentricity of the Keplerian orbits constrains the algorithm and forces it to take shorter timesteps. The analysis is applied to the solar system and other problems. |
| |
Keywords: | Ordinary differential equations nearly integrable systems Keplerian orbits Hamiltonian |
本文献已被 SpringerLink 等数据库收录! |
|