Solution of Approximate Equations

Abstract

In this chapter we wish to explore some of the ideas surrounding approximate equations. The basic idea is the following: if we are confronted with a nonlinear differential equation whose solution is unknown, then we would like to replace this equation with a set, one or more, of approximating equations whose solutions are known. Our goal is to see if we can obtain an approximate solution to the nonlinear system by exact solutions to the approximating equation. Since we are, in fact, approximating one differential equation by a set of others, this chapter considers the interrelations between them.