摘要
本文用辛积分方法对动力天文中三种典型的动力模型作了大量数值计算。计算结果表明,与一般非辛数值积分方法相比,辛积分方法在动力天文的定性研究中具有独特的优越性。
Symplectic integrators developed recently within the framework of symplectic geometry are some numerical methods for Hamiltonian system. Symplectic difference schemes preserve ex- actly symplectic structure, which is one of the most important features for Hamiltonian phase flows. In this paper, we choose the Runge-Kutta algorithms as a representative of all non-symplectic algorithms, and compare numerical results of symplectic and non-symplectic algorithms from several different aspects by practical numerical calculations with three typical models in dynamical astronomy. In order to reflect the differences between RK and SI more clearly, all numerical results appearing in this paper are presented in the forms of tables and figures. These computational results show that SI4 is superior to RK4 in computational efficiency, and the accumulation of numerical errors in Hamiltonian functions by symplectic integrators does not have a secular term. The most remarkable is that symplectic integrators preserve the innate geometrical features of the phase space of a Hamiltonian system without being polluted and distorted for the sake of calculation after a very long period. In the meantime, from these computations we are aware that symplectic integrators are a more reliable method in compari- son with the RK algorithm if one needs investigate the features of regular and chaotic motions. In a word, numerical results show a strong evidence of superior performance of symplectis schemes over all non-symplectic ones. In particular, symplectic integrators have a great, ad- vantage over the qualitative investigation of dynamical astronomy compared with the general non-symplectic numerical methods. An extensive appliaction of symplectic integrators in dy- namical astronomy is in prospect.
出处
《天文学报》
CSCD
北大核心
1992年第1期36-47,共12页
Acta Astronomica Sinica
基金
国家自然科学基金
关键词
动力天文
辛结构
辛算法
应用
Symplectic structure
Symplectic integrator
Dynamical astronomy
