On an asymptotic method for computing the modified energy for symplectic methods
On an asymptotic method for computing the modified energy for symplectic methods
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DOI：
10.3934/dcds.2014.34.1105
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发表时间：
2013-04
影响因子：
1.1
通讯作者：
P. C. Moan;Jitse Niesen
中科院分区：
文献类型：
--
作者：
P. C. Moan;Jitse Niesen
我们重新审视了Skeel等人的算法。[5，16]用于计算与Hamilton系统的辛离散相关的修改的或阴影的能量。我们修改的算法使用Richardson外推，以获得任意高的精度。误差估计表明，新的方法捕获的指数小漂移与这样的离散。几个数值例子说明了这一理论。
We revisit an algorithm by Skeel et al. [5,16] for computing the modified, or shadow, energy associated with symplectic discretizations of Hamiltonian systems. We amend the algorithm to use Richardson extrapolation in order to obtain arbitrarily high order of accuracy. Error estimates show that the new method captures the exponentially small drift associated with such discretizations. Several numerical examples illustrate the theory.