Finite Difference Solutions of Maxwell's Equations in Three Dimensions

The method of finite differences is used successfully to solve elliptic second-order partial differential equations. For Laplace's equation ((DELTA)E = 0) and Poisson's equation ((DELTA)E = G x,y,z ), there is little difficulty in applying finite difference equations. However, for the Helmholz equation ((DELTA)E + k('2)E = 0), which is derived from Maxwell's equations, there has arisen problems which have limited application of this method. The objective of this dissertation is to investigate these problems and suggest ways to alleviate them. Included is an analysis of the numerical errors, an example of an application to microwave circuits, a discussion of other applications to specific problems and suggestions for future work to be done in this field.