A family of symplectic integrators: Stability, accuracy, and molecular dynamics applications
A family of symplectic integrators: Stability, accuracy, and molecular dynamics applications
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DOI：
10.1137/s1064827595282350
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发表时间：
1997-01-01
影响因子：
3.1
通讯作者：
Schlick, T
中科院分区：
文献类型：
--
作者：
Skeel, RD;Zhang, GH;Schlick, T
研究了特殊二阶常微分方程的几种积分方法：蛙跳法、隐式中点法、梯形法、Stormer-Verlet法和Cowell-Numerov法。我们表明，所有的成员，或相当于成员，一个参数的家庭计划。有些方法有一个以上的共同形式，我们讨论这些形式的系统枚举。我们还提出了一个稳定性和准确性分析的基础上的思想“修改方程”和辛性的证明。因此，Cowell-Numerov和'' LIM 2 ''（由Zhang和Schlick提出的方法）是辛的。对这些积分器使用的值的不同解释导致更高的精度和更好的节能。因此，我们认为，简单的能量守恒分析是误导。
The following integration methods for special second-order ordinary differential equations are studied: leapfrog, implicit midpoint, trapezoid, Stormer-Verlet, and Cowell-Numerov. We show that all are members, or equivalent to members, of a one-parameter family of schemes. Some methods have more than one common form, and we discuss a systematic enumeration of these forms. We also present a stability and accuracy analysis based on the idea of ''modified equations'' and a proof of symplecticness. It follows that Cowell-Numerov and ''LIM2'' (a method proposed by Zhang and Schlick) are symplectic. A different interpretation of the values used by these integrators leads to higher accuracy and better energy conservation. Hence, we suggest that the straightforward analysis of energy conservation is misleading.