2.6 A Numerical Method

INTRODUCTION

In Section 2.1 we saw that we could glean qualitative information from a first-order DE about its solutions even before we attempted to solve the equation. In Sections 2.2–2.5 we examined first-order DEs analytically; that is, we developed procedures for actually obtaining explicit and implicit solutions. But many differential equations possess solutions and yet these solutions cannot be obtained analytically. In this case we “solve” the differential equation numerically; this means that the DE is used as the cornerstone of an algorithm for approximating the unknown solution. It is common practice to refer to the algorithm as a numerical method, the approximate solution as a numerical solution, and the ...

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