An Example of Computer Enhanced Analysis

Abstract

In this report, a first order nonlinear partial differential equation with a parameter dependent initial condition is examined. Even though an analytic solution of the equation is determined, a surprising bifurcation phenomenon is discovered via computer graphics. This “computer-discovered” bifurcation, in turn, leads to further mathematical analysis and deeper geometric understanding of the solution. Indeed, this is a simple example of an elementary catastrophe (in the sense of Thorn) and demonstrates the usefulness of numerical computations in providing qualitative information even in the presence of exact solutions.