ABSTRACT
In Chapter 1, Section 1, we reviewed the mathematical forms of the ODEs commonly used in scientific and engineering applications, i.e., explicit, semi-implicit, and implicit initial and boundary value ODEs. ODEs are a natural way to express many physical problems, and we routinely write sets of ODEs which can number in the hundreds or thousands. Prior to the development of digital computers, this would have been an academic exercise since we would have had no way to solve such large sets of equations (recall again that the most we can do with analytical methods is about four linear, constant coefficient ODEs). Now, however, with the digital computer this bottleneck has been eliminated, and we are essentially limited only by our imagination in writing ODE models. In principle we can solve any ODE model using numerical integration. Obviously, then, we require some knowledge of numerical integration of ODEs to use digital computers effectively; this is topic of this chapter.
