ABSTRACT
The method of lines (MOL) is a well-established numerical technique for the analysis of transmission lines, waveguide structures, and scattering problems. It basically involves discretizing a given differential equation in one or two dimensions while using analytical solution in the remaining direction. Although the method of lines is commonly used in the electromagnetics (EM) community for solving hyperbolic (wave equation), it can be used to solve parabolic and elliptic equations. This chapter considers the application of MOL to solve Laplace's equation (elliptic problem) involving two-dimensional rectangular and cylindrical regions. It illustrates the use of MOL to solve Laplace's equation in cylindrical coordinates by applying discretization procedure in the angular direction. The resulting coupled ordinary differential equations are decoupled by matrix transformation and solved analytically. In fact, MOL can also be used to solve parabolic equations. The chapter describes the use of MOL to solve hyperbolic Maxwell's equations in the time-domain.
