一类Rayleigh方程的渐近解与精度估计

The Asymptotic Solution and Estimate of Precision for a Class of Rayleigh Equations

本文利用摄动理论和方法,讨论了一类Rayleigh方程的奇摄动问题.相应于参数q=0和q=0,分别得出了该类问题解的渐近表达式.并将结果应用于两个例子的求解.通过对渐近解与精确解进行比较,显示了所得渐近解达到了较高精度.最后,将结果应用于原液压模型,得出的结论与相关参考文献中得出的结论一致.本文所采用的方法为解决相关类型的非线性问题提供了一种较为有效的方法.

By using the theory and method of perturbation,a class of singularly perturbed problems for Rayleigh equations is discussed.Under the parameters of the problems q = 0 and q = 0,the asymptotic approximations of the solutions with respect to the problems are obtained.The results are further applied to two specific examples,as compared the asymptotic solutions with exact solutions.It is substantiated that the asymptotic expression of the solutions attains a higher precision.Finally,the obtained result is applied to solving the original hydraulic model,and the conclusions are consistent with that from experimentation.The obtained result is meaningful in solving some similar nonlinear equations.