Explicit difference equations are presented for the solution of a signal of arbitrary waveform propagating in an holmic dielectric, cold plasma, a Debye model dielectric, and a Lorentz model dielectric These difference equations are derived from the governing timedependent integro-differential equations for the electric fields by a finite difference method. A special difference equation is derived for the grid point at the boundary of two different media. Employing this difference equation, transient signal propagation in an inhomogeneous media can be solved provided that the medium is approximated in a step-wise fashion. The solutions are generated simply by marching on in time. By appropriate choice of the time and space intervals, numerical stability and convergence are always obtained. Numerous examples are given to demonstrate the wide range of applicability of the difference solution. These include: the transmission and reflection of an electromagnetic pulse normally incident on a multilayered holmic dielectric;a step-modulated sine wave propagating in a dispersive media, a problem originally considered by Somerfield and Brillouih;the reflection of a short Gaussian pulse normally incident on inhomogeneous lossy cold plasma with a longitudinal d.c. magnetic field, and many others. It is concluded that while the classical transform methods will remain useful in certain cases, with the development of the finite difference methods described in this dissertation, an extensive class of problems of transient signal propagating in stratified dispersive media can be effectively solved by numerical methods.
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