Volume-preserving algorithms for source-free dynamical systems
Volume-preserving algorithms for source-free dynamical systems
复制标题
DOI：
10.1007/s002110050153
复制
发表时间：
1995-10
影响因子：
2.1
通讯作者：
Feng Kang;Zai-jiu Shang
中科院分区：
文献类型：
--
作者：
Feng Kang;Zai-jiu Shang
本文首先阐述了为什么体积保持算法适用于无源系统的数值求解，然后证明了所有传统的方法都不是体积保持的。其次，在将无源矢量场分解为基本二维哈密顿场的有限和的基础上，将相应的基本辛格式组合成一个基本保体差分格式，给出了构造无源系统保体差分格式的一般方法。最后，我们对可构造任意高阶显式可逆保体积方案的所谓可分离无源系统作了一些特殊讨论。
In this paper, we first expound why the volume-preserving algorithms are proper for numerically solving source-free systems and then prove all the conventional methods are not volume-preserving. Secondly, we give a general method of constructing volume-preserving difference schemes for source-free systems on the basis of decomposing a source-free vector field as a finite sum of essentially 2-dimensional Hamiltonian fields and of composing the corresponding essentially symplectic schemes into a volume-preserving one. Lastly, we make some special discussions for so-called separable source-free systems for which arbitrarily high order explicit revertible volume-preserving schemes can be constructed.