Comparison of different numerical methods for solving boundary-value problems in electromagnetics

A review of various techniques for the approximate solution of boundary-value problems is presented. The analysis is based on a simple one-dimensional example. A differential equation describing steady-state voltage distribution along a transmission line excited by a dc source was taken as the example. The problem was solved by the commonly applied methods of moments and by the variational Ritz method using polynomial and trigonometric approximations. The specific features of the methods applied are discussed. Although the example does not deal with wave propagation, it is valuable for teaching numerical methods in electromagnetics.