High-precision Runge-Kutta method for transmission line equation
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摘要: 提出了一种求解传输线方程的高精度龙格-库塔（RK）方法。此方法在空间上采取高阶泰勒展开，提高了对空间微分的近似精度，减少了数值色散所带来的误差。与传统的时域有限差分法（FDTD）方法相比，在每波长采样数相同时，RK方法的计算精度更高。同时，根据Taylor模型，对外界平面波激励源进行离散，成功利用RK方法对外部场激励传输线进行求解，扩大了龙格−库塔方法在求解传输线方程时的应用范围。通过编程对平面波辐照下无限大地平面上的单导体与双导体的算例分别应用FDTD方法与RK方法进行了计算，验证了RK方法的正确性。结果表明同等计算条件下RK方法的计算精度更高。Abstract: This paper presents a high-precision Runge-Kutta (RK) method for solving transmission line equations. This method adopts high-order Taylor expansion in space, which improves the approximation accuracy of spatial differentiation. Compared with the traditional finite element time-domain method, when the number of samples per wavelength is the same, RK method has higher precision. At the same time, according to the Taylor model, researchers use RK method to solve transmission line equation in the external field excitation. The correctness and high precision of the RK method are verified by numerical examples of our study.
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Key words:
- Runge-Kutta /
- field-line coupling /
- transmission line /
- FDTD /
- Taylor expansion
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