Simulation of the transmission line equation by a high-order FDTD method

Abstract

This note deals with transmission lines equation. The frequency dependent parameters which are often considered constants to ease the numerical implementation, are actually taken for their real physical state. We aim to obtain a physical solution of the equation by a high order scheme. The proposed scheme is an enhanced version of FDTD methods, which are known to be powerful tools for solving equations of this alike. In particular, the scheme is built to deal with oscillations of the load voltage. The oscillations that are a result of the taking-over of the hyperbolic characteristic of the equation are corrected by a high order relaxed FDTD method and a regularizing effect of Runge Kutta. We validate our theoretical results by few numerical simulations.