| 何吉欢.无小参数非线性振动方程的近似方法[J].南华大学学报(自然科学版),2000,(1):.[.Approximate Solution for Some Nonlinear Oscillation Equations without Small Parameters[J].Journal of University of South China(Science and Technology),2000,(1):.] |
| 无小参数非线性振动方程的近似方法 |
| Approximate Solution for Some Nonlinear Oscillation Equations without Small Parameters |
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| DOI： |
| 中文关键词: 变分迭代算法,变分原理,拉氏乘子,非线性 |
| 英文关键词:variational iteration method,variational principle,Lagrange multiplier,nonlinearity |
| 基金项目:上海市教委青年基金! ( 98QA47)，上海市科委启明星项目资助 |
| 何吉欢 |
| 上海大学应用数学和力学研究所!上海200072 |
| 摘要点击次数: 690 |
| 全文下载次数: 2 |
| 中文摘要: |
| 本文提出了一种求解非线性方程的迭代算法 ,它不依赖于小参数 ,是先给方程一个带待定函数的试函数作为初始近似解 ,然后用拉氏乘子法构造一个迭代公式 (校正泛函 ) .试函数中的待定函数可用变分直接方法确定 ,而校正泛函中的拉氏乘子可用变分理论最佳确定 .应用这种方法不会出现长期项 ,其结果表明这种新方法是比较有效的 . |
| 英文摘要: |
| In the paper,an iteration method has been proposed to solve analytically some nonlinear oscillation equations.In this method,without depending upon small parameter,a trial function with possible unknowns is used as initial approximation,then a correction functional is constructed by means of a general Lagrange multiplier,which can be identified via variational theory.The unknown constant in the trial function can be determined by direct variational method (such as least squares method).Some examples have been given,revealing that the new method is very effective and convenient. |
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