摘要
模方程根的求解是甚低频场量计算的关键。本文基于波导模理论,分别采用基于改进欧拉法和龙格-库塔法的微分方程数值解法、牛顿迭代法和欧拉-牛顿迭代法求解了不同传播信道下的模方程根。结果表明:(1)微分方程数值解法的计算精度受限于计算步长,步长越小,精度越高,但耗时过长;(2)牛顿迭代法计算速度快,但对初始值的过度依赖使其存在无法收敛的情况;(3)欧拉-牛顿迭代法通过对初值预处理,在保证较高模方程根求解精度和可靠性的同时,拥有更高的求解效率。
The solution of modal equation roots is the key of very low frequency(VLF)field quantity calculation.In this paper,based on the theory of waveguide mode,the numerical method of differential equation(i.e.the improved Euler method and the Runge-Kutta method),the Newton’s method and the Euler-Newton’s method are used to solve the modal equation roots under different propagation channels.The results show that:(i)The calculation accuracy of the numerical method of the differential equation is limited by the calculation step size,the smaller the step size,the higher the precision,but the calculation time is too long;(ii)Newton’s method has a fast calculation speed,but the over-dependence on the initial value makes it possible to non-converge;(iii)The Euler-Newton’s method has higher solving efficiency by pre-processing the initial value and ensuring the higher accuracy and reliability of the modal equation roots.
作者
蒲玉蓉
韩雪妮
王丹丹
席晓莉
Pu Yurong;Han Xueni;Wang Dandan;Xi Xiaoli(School of Automation and Information Engineering,Xi’an University of Technology,Xi’an 710048,China)
出处
《科技通报》
2020年第12期1-7,36,共8页
Bulletin of Science and Technology
基金
十三五装备预研领域基金(No.6140518020205)
中国博士后基金(No.2015M582687)
国家自然科学基金(No.61771389)
关键词
甚低频
模方程的根
改进欧拉法
龙格-库塔法
牛顿迭代法
very low frequency(VLF)
roots of modal equation
improved Euler method
Runge-Kutta method
Newton’s method
