Exactly Conservative Integrators
Exactly Conservative Integrators
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精确保守积分器
DOI：
10.1137/s0036139995289313
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发表时间：
1995
期刊：
影响因子：
--
通讯作者：
P. Morrison
中科院分区：
文献类型：
--
作者：
B. Shadwick;J. Bowman;P. Morrison
保守系统的传统显式数值离散一般预测任何非线性不变量的人工长期漂移。在这项工作中，我们提出了一个通用的方法来开发明确的非传统算法，保存这样的不变量。我们说明了它的三波截断的欧拉方程，Lotka-沃尔泰拉捕食模型，开普勒问题的方法。辛（相位-空间守恒）的集成方法以及非辛保守的方法的背景下，讨论的想法。我们评论我们的方法一般保守系统的应用。
Traditional explicit numerical discretizations of conservative systems generically predict artificial secular drifts of any nonlinear invariants. In this work we present a general approach for developing explicit nontraditional algorithms that conserve such invariants exactly. We illustrate the method by applying it to the three-wave truncation of the Euler equations, the Lotka--Volterra predator-prey model, and the Kepler problem. The ideas are discussed in the context of symplectic (phase--space-conserving) integration methods as well as nonsymplectic conservative methods. We comment on the application of our method to general conservative systems.