6.1 Euler Methods and Error Analysis

6.2 Runge–Kutta Methods

6.3 Multistep Methods

6.4 Higher-Order Equations and Systems

6.5 Second-Order Boundary-Value Problems

Chapter 6 in Review

A differential equation need not possess a solution. But even when a solution exists, we may not be able to exhibit it in an explicit or implicit form; we may have to be content with an approximation to the solution. In this chapter we continue to explore the basic idea introduced in Section 2.6, that is, using the differential equation to construct an algorithm to approximate the y-coordinates of points on the actual solution curve.