摘要
改进的Lindstedt-Poincar啨(L-P)法在传统的L-P法的基础上,对频率的展开式作了改进;卷积分法则提供了一个求近似解的迭代格式.本文首先用这两种方法求得平方非线性振动方程的二阶渐近解,并用Picard逐步逼近法证明由卷积分法得到的渐近解在有限的时间上是一致收敛的.其次,一种数值阶验证技术证实求得的二阶渐近解对小参数都是一致有效的.最后,对这两种渐近解进行误差的数值比较,结果表明它们对大参数无效,并简明分析其失效的原因.因此,这两种方法在平方非线性振动方程中的应用受到小参数的限制.
The modified Lindstedt-Poincar6 method modifies the expansion of the fundamental frequency based on the classical L-P method, and the convolution integral method provides an iteration scheme to obtain the asymptotic solution. Firstly, we obtained the second order solutions of a quadratic nonlinear oscillator respectively by these two methods, and demonstrated that the solution obtained by convolution integral was uniformly convergent. Secondly, a technique of numerical order verification was applied to verify that the asymptotic solutions were uniformly valid for small parameter. Finally, numerical comparison of error shows that this two methods are invalid for large parameter. So, these two methods are limited by small parameter when they are applied to quadratic nonlinear oscillator.
出处
《动力学与控制学报》
2006年第3期242-246,共5页
Journal of Dynamics and Control
关键词
非线性振动
改进的L-P法
卷积分法
数值验证
nonlinear oscillation, modified Lindstedt-Poincaré method, convolution integral method, numerical verification
