相对论谐振子解析逼近解的构造

J4 ›› 2013, Vol. 51 ›› Issue (01): 83-88.

相对论谐振子解析逼近解的构造

孟艳平¹, 孙维鹏², 张皆杰²

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

收稿日期:2012-05-02 出版日期:2013-01-26 发布日期:2013-01-31
通讯作者: 孙维鹏 E-mail:sunwp@jlu.edu.cn

Construction of Analytical Approximate Solutionsto Relativistic Harmonic Oscillators

MENG Yanping¹, SUN Weipeng², ZHANG Jiejie²

1. College of Mechanical Engineering, Changchun Institute of Technology, Changchun 130012, China;2. College of Mathematics, Jilin University, Changchun 130012, China

Received:2012-05-02 Online:2013-01-26 Published:2013-01-31
Contact: SUN Weipeng E-mail:sunwp@jlu.edu.cn

摘要/Abstract

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.

关键词: 相对论谐振子；牛顿谐波平衡法；解析逼近解

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 whole range of initial oscillation amplitudes. The approximate periods and periodic solutions are excellently agreed with the exact ones.

Key words: relativistic harmonic oscillators, Newtonharmonic balance method, analytical approximation

中图分类号:

O322

孟艳平, 孙维鹏, 张皆杰. 相对论谐振子解析逼近解的构造[J]. J4, 2013, 51(01): 83-88.

MENG Yan-Beng, SUN Wei-Feng, ZHANG Jie-Jie. Construction of Analytical Approximate Solutionsto Relativistic Harmonic Oscillators[J]. J4, 2013, 51(01): 83-88.