ABSTRACT
This chapter presents a classification of partial differential equations encountered in the mathematical formulation of heat, mass, and momentum transfer problems, and discusses the physical significance of such a classification in relation to the numerical solution of the problem. There is a wide variety of engineering problems that are governed by partial differential equations of the parabolic type. The problems of steady-state diffusion, convection–diffusion, and some fluid flow problems are governed by partial differential equations that are elliptic. An understanding of the behavior of a system of equations, namely, whether it is hyperbolic or elliptic, is important in the selection of an appropriate finite difference scheme for its solution. In many engineering applications, the physical processes are governed by a system of equations rather than by a single equation. In some situations, a higher-order partial differential equation can be converted into a system of first-order equations.
