36 - Reduction of PDEs to a First Order System

Abstract

This chapter describes the reduction of partial differential equations (PDEs) to a first-order system. By introducing variables to represent the derivatives in a partial differential equation, a first-order system may be obtained. Sometimes it is advantageous to reduce a partial differential equation of high order for a single unknown function to a system of several first-order equations. This might be done, for instance, to utilize a specific numerical package that requires a partial differential equation to be input as a first-order system. This can always be done by introducing an appropriate set of derivatives as unknowns. The general procedure is to introduce new variables as the derivatives of the desired function, and then discover relations among these functions. Systems of high order partial differential equations can also be made into first-order systems, by the introduction of enough terms.