3. Theory of Ordinary Differential Equations

The theory of numerical methods for ordinary differential equations is closely associated with certain aspects of the analytic theory of these equations. These aspects are highlighted in this chapter, which is the last preparatory chapter of the book. In the first section, we dispense with some of the more basic theoretical considerations concerning solutions of initial and boundary value problems. Some fundamental existence and uniqueness results are given. Of course, our purpose here is not to duplicate the efforts of a basic text in ODEs. Thus we merely review these results.