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

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 .

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.