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| 辛欧拉格式形式能量的收敛性 | |
| 引用本文： | 戴桂冬,赵艳敏,聂宁明.辛欧拉格式形式能量的收敛性[J].系统仿真学报,2010,22(2). |
| 作者姓名： | 戴桂冬 赵艳敏 聂宁明 |
| 作者单位： | 1. 北京服装学院基础教学部,北京,100029 2. 许昌学院数学科学学院,许昌,461000 3. 中国科学院数学与系统科学研究院计算数学与科学工程计算研究所,北京,100190;中科院研究生院,北京,100190 |
| 基金项目： | 北京服装学院引进人才院内科研项目(2007A-15); 国家自然科学基金(10471145,10672143); 中国科学院科学与工程计算国家重点实验室开放合作课题(K81Z12127F) |
| 摘 要： | 对谐振子系统和单摆系统分析了辛欧拉格式形式能量的收敛性。得到辛欧拉格式的形式能量后,发现应用于谐振子系统的辛欧拉格式的形式能量是收敛的,对单摆系统无法确定形式能量的收敛范围,但其修正方程精确保持系统的平衡点。理论分析和数值模拟表明在形式能量收敛的条件下,用辛欧拉格式计算这两个系统具有保持整体结构的效果。 |
| 关 键 词： | 谐振子系统 单摆系统 辛欧拉格式 形式能量 |
Convergency of Formal Energy for Symplectic Euler Scheme |
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| DAI Gui-dong,ZHAO Yan-min,NIE Ning-ming.Convergency of Formal Energy for Symplectic Euler Scheme[J].Journal of System Simulation,2010,22(2). | |
| Authors: | DAI Gui-dong ZHAO Yan-min NIE Ning-ming |
| Institution: | DAI Gui-dong1,ZHAO Yan-min2,NIE Ning-ming3,4 (1.Element Department of Beijing Institute of Fashion Technology,Beijing 100029,China,2.School of Mathematical Sciences,Xuchang University,Xuchang 461000,3.Institute of Computational Mathematics , Scientific/Engineering Computing,Academy of Mathematics & Systems Science Chinese Academy of Sciences,Beijing 100190,4.Graduate School of Chinese Academy of Sciences,China) |
| Abstract: | The convergency of the formal energy of symplectic Euler scheme for harmonic oscillator system and simple pendulum system was considered.The formal energy of symplectic Euler scheme was proposed,and its convergency was obtained when the scheme was applied to harmonic oscillator system.And,the equilibrium points of simple pendulum system were preserved by the scheme.Theoretical analysis and numerical simulation show that symplectic Euler scheme preserves the whole structure of the two systems when the formal... |
| Keywords: | harmonic oscillator system simple pendulum system symplectic Euler scheme formal energy |
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