一类非线性振动方程解的研究  

RESEARCH ON THE SOLUTION OF ONE KIND OF NONLINEAR OSCILLATION EQUATION

作　　者：何敏[1] 朱诵文[1] 王其申[1] 

机构地区：[1]安庆师范学院数学与计算科学学院,安徽安庆246011

出　　处：《巢湖学院学报》2008年第6期27-29,共3页Journal of Chaohu University

摘　　要：本文探讨一类非线性振动方程的解法。参考文献[1]给出的非线性微分方程属于一维的情况,在假定势能函数对平衡位置是对称的情况下,采用逐步近似法求解了方程,给出三次谐波项的系数。本文在此基础上用这种方法求解五次谐波项的系数,并以此为例说明可以继续求解更高阶奇次谐波项的系数从而得到更精确的解。In this paper we discussed the solution d one kind of nonlinear oscillation equation.Reference one give a nonlinear differential equation at the condition of one dimension.Assuming that potential energy function is symmetrical to balance position,we used step approximation solution to solve the equation,and get the coefficient of the thrice harmonic term.On this foundation we continued to use the method to solve the coefficient of the quintic harmonic term and used this exemple to explain that we can continue to solve the coefficient of high-level harmonic term,thereby we can gain more precise solution.

关 键 词：非线性振动方程 逐次近似解法 

分 类 号：O241.8[理学—计算数学]