辛算法应用于Duffing方程的保结构性 |
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引用本文: | 王玲书,冯光辉. 辛算法应用于Duffing方程的保结构性[J]. 军械工程学院学报, 2008, 20(1): 72-74 |
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作者姓名: | 王玲书 冯光辉 |
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作者单位: | 王玲书(河北经贸大学数学与统计学学院,河北,石家庄,050061;军械工程学院基础部,河北,石家庄,050003);冯光辉(军械工程学院基础部,河北,石家庄,050003) |
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基金项目: | 国家自然科学基金资助项目(编号10571173) |
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摘 要: | 讨论了不受外力的Duffing方程在辛算法和非辛算法作用下,相轨线被保持和破坏的性质。证明了当时间步长充分小时,辛算法可以保持原系统的大部分不变闭曲线,而非辛算法却做不到这一点。
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关 键 词: | Duffing方程 辛算法 不变闭曲线 |
文章编号: | 1008-2956(2008)01-0072-03 |
修稿时间: | 2007-10-05 |
Structure-Preserving Properties of Symplectic Algorithms for Duffing Equation |
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Affiliation: | WANG Ling-shu, FENG Guang-hui(1. College of Mathematics and Statistics, Hebei University of Economics & Business, Shijiazhuang 050061, China; 2. Department of Basic Courses, Ordnance Engineering College, Shijiazhuang 050003, China) |
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Abstract: | In this paper, we discuss the properties of the phase orbits of Duffing equation that are preserved or destroyed under symplectic and non-symplectic discretizations. We prove that symplectic algo- rithms may keep most of the invariant curves of Duffing equation when the time-step is small enough but non-symplectic algorithms cannot. |
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Keywords: | Duffing equation symplectic algorithms invariant curve |
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