94 - Method of Characteristics

Abstract

This chapter elaborates method of characteristics applicable to systems of quasi-linear partial differential equations. Systems of quasi-linear partial differential equations are one or more partial differential equations linear in the first derivatives of the dependent variables, with no higher order derivatives present. If the initial data is not given along a characteristic, then an exact solution can be obtained (generally implicit). A quasi-linear partial differential equation can be transformed into a set of ordinary differential equations that define the characteristics, and a set of ordinary differential equations that describe how the solution changes along any specific characteristic. This technique extends naturally to systems of partial differential equations, with virtually no increase in complexity. This allows a single partial differential equation of higher order (and hyperbolic type) to be analyzed.