Summary form only given. Detailed determinations of the electron velocity distribution function are becoming more common due to the greater availability of computational power. Some of the classical problems in ionized gas physics are found to be in need of such analysis. Generally, these solutions are derived from statistical techniques, such as Monte-Carlo, or from quasi-particle methods, such as PIC, and are essentially time-dependent methods which represent the convective effects in a very "physical" way. In contrast, the continuum approaches to hyperbolic PDE solutions, which have a strong "mathematical" basis and have experienced significant advances in recent years, have been difficult to apply to the Boltzmann equation. These methods have several important advantages such as their ability to resolve steep gradients, including discontinuous behavior, and their uniform accuracy across the domain due to their non-statistical nature. Furthermore, in situations where simultaneous solution of several quantities is desired, and some are best described in the continuum, it is convenient if the same solver can be used for all. Techniques for enabling the application of these methods to the Boltzmann equation will be described.