A Monte Carlo algorithm is derived to solve the one-dimensional telegraph equations in a
bounded domain subject to resistive and non-resistive boundary conditions. The proposed
numerical scheme is more efficient than the classical Kac’s theory because it does not
require the discretization of time. The algorithm has been validated by comparing the
results obtained with theory and the Finite-difference time domain (FDTD) method for
a typical two-wire transmission line terminated at both ends with general boundary
conditions. We have also tested transmission line heterogeneities to account for wave
propagation in multiple media. The algorithm is inherently parallel, since it is based on
Monte Carlo simulations, and does not suffer from the numerical dispersion and dissipation
issues that arise in finite difference-based numerical schemes on a lossy medium. This
allowed us to develop an efficient numerical method, capable of outperforming the classical
FDTD method for large scale problems and high frequency signals.