论文标题
放松哈密顿问题的runge-kutta方法
Relaxation Runge-Kutta Methods for Hamiltonian Problems
论文作者
论文摘要
最近引入的runge-kutta方法的放松方法可用于在汉密尔顿系统的整合中执行能量保护。在这种情况下，我们研究了隐式和显式松弛runge-kutta方法的行为。我们发现，除了其有用的保护特性外，放松方法还带来了其他改进。实验表明，它们的解决方案与真实解决方案具有更强的定性相似性，并且误差随着时间的流逝而增长。我们还证明，对于某些类别的哈密顿系统，这些方法是超浓缩的。
The recently-introduced relaxation approach for Runge-Kutta methods can be used to enforce conservation of energy in the integration of Hamiltonian systems. We study the behavior of implicit and explicit relaxation Runge-Kutta methods in this context. We find that, in addition to their useful conservation property, the relaxation methods yield other improvements. Experiments show that their solutions bear stronger qualitative similarity to the true solution and that the error grows more slowly in time. We also prove that these methods are superconvergent for a certain class of Hamiltonian systems.
