The numerical solution of the transmission line wave equation is examined using the transmission line model of a lightning return stroke (LRS) taken as a case study. The LRS is represented by a transverse electromagnetic wave travelling at a velocity close to the velocity of light along a highly ionized lightning leader channel. The leader channel is modeled as a lossy transmission line. Attempts to model the lightning return stroke by an electric circuit in order to determine the currents and radiated electromagnetic fields is categorized as the distributed transmission line model (DTLM). The DTLM method in turn may be subdivided into two categories: Distributed inductance (L), capacitance (C) and resistance (R) model (DLCRM) and the lumped LCR model (LCRM). In this brief communication, we indicate some pitfalls to watch out for in solving for the transmission line wave equationusing numerical methods, and how these may be avoided. Furthermore, we propose tests that may be applied, including the analytical solution of diffusion waves, to ensure the stability and accuracy of the numerical solution DLCRM simulations. Key words: Finite difference time domain method, numerical solution of transmission line wave equation, lightning return stroke model, lightning radiated electromagnetic fields.