ABSTRACT
This chapter shows that the type of partial differential equation that occurs for problems involving wave propagation differ from those that represent elastic behavior and from those that represent heat transfer processes. In fact, it is those differences that direct the type of solution approach that is used to solve for the state variables that are unknown in those physical applications. The chapter describes hyperbolic differential equations and the solution processes that must be used to solve for the physical variables. It explores an abbreviated manner, one of the most powerful approaches that a researcher can take toward the numerical simulation of hyperbolic differential equations. The method of characteristics therefore provides a solution approach for all kinds of hyperbolic differential equations, regardless of whether a discontinuity in the solution variables exists. The chapter suggests that the methods are only a small portion of the actual techniques that may be used when the method of characteristics is used.
