| 相对论谐振子解析逼近解的构造 |
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| 引用本文： | 孟艳平,孙维鹏,张皆杰.相对论谐振子解析逼近解的构造[J].吉林大学学报(理学版),2013,51(1):83-88. |
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| 作者姓名： | 孟艳平 孙维鹏 张皆杰 |
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| 作者单位： | 1. 长春工程学院 机电学院, 长春 130012； 2. 吉林大学 数学学院, 长春 130012 |
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| 基金项目： | 国家自然科学基金(批准号:51005196) |
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| 摘 要： | 利用牛顿谐波平衡法构造相对论谐波振子的解析逼近周期和周期解. 先引入新变量, 重写关于新变量的控制方程, 再用牛顿谐波平衡法求解. 结果表明: 该方法具有较快的收敛速度; 得到的解析逼近解在振幅全部取值范围内均有效; 构造的解析逼近周期和周期解具有较高的精度.
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| 关 键 词： | 相对论谐振子 牛顿谐波平衡法 解析逼近解 |
| 收稿时间： | 2012-05-02 |
Construction of Analytical Approximate Solutions to Relativistic Harmonic Oscillators |
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| MENG Yan-ping,SUN Wei-peng,ZHANG Jie-jie.Construction of Analytical Approximate Solutions to Relativistic Harmonic Oscillators[J].Journal of Jilin University: Sci Ed,2013,51(1):83-88. |
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| Authors: | MENG Yan-ping SUN Wei-peng ZHANG Jie-jie |
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| Institution: | 1. College of Mechanical Engineering, Changchun Institute of Technology, Changchun 130012, China;2. College of Mathematics, Jilin University, Changchun 130012, China |
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| Abstract: | The Newton harmonic balance method was used to construct analytical approximate periods and periodic solutions to the relativistic harmonic oscillator. Introducing a new variable and rewriting the control equation in terms of the new variable, we applied the Newton-harmonic balance method to solving the resulted equation. The method yields rapid convergence with respect to exact solution, and the analytical approximations obtained are valid for the wholerange of initial oscillation amplitudes. The approximateperiods and periodic solutions are excellently agreed with the exact ones. |
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| Keywords: | relativistic harmonic oscillators Newton harmonic balance method analytical approximation |
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