传输线方程高精度直接积分的数值求解方法*

High Precision Numerical Method for Direct Integration of Transmission Line Equation

  • 摘要: 提出一种基于精细积分法与时域微分求积法相结合的传输线方程的数值求解方法。首先将传输线方程采用基于紧致有限差分法的四阶差分格式进行空间离散,得到关于时间的一阶线性常微分方程组,四阶差分格式对于空间微分有很好的近似精度。然后利用精细积分法与微分求积法对一阶线性常微分方程组进行数值求解。通过理论分析可知,与传统的传输线方程数值求解方法——时域有限差分法(Finite difference time domain, FDTD)相比,所提方法不涉及到状态矩阵求逆运算,保证了数值求解精度,并且其数值稳定性与计算时间、空间步长无关,可采用大步长进行数值计算,能够有效提高计算效率。最后利用仿真实例进行算法验证,结果显示,相比于时域有限差分法,所提方法能够抑制数值振荡,提高了计算精度。

     

    Abstract: A numerical solution method for the transmission line equation based on the combination of the precise integration method and the time-domain differential quadrature method is proposed. First, the transmission line equation is spatially discretized by a fourth-order difference scheme based on the compact finite difference method, and the first-order linear ordinary differential equations about time are obtained. The fourth-order difference scheme has good approximate accuracy for spatial differentiation. Then, the precise integration method and differential quadrature method are used to numerically solve the first-order linear ordinary differential equations. Through theoretical analysis, compared with the traditional numerical solution method for transmission line equations, finite difference time domain(FDTD), this proposed method does not involve state matrix inverse operations, guarantees the accuracy of the numerical solution, and its numerical stability has nothing to do with the calculation time and space step. It can be used numerical calculations with large steps can effectively improve calculation efficiency. Finally, a simulation example is used to verify the algorithm. The results show that compared with the finite difference time domain method, this proposed method can suppress numerical oscillations and improve the calculation accuracy.

     

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