For engineering analysis it is always preferable to develop explicit equations that include symbols, but this is not always practical. In cases where the equations are too costly to develop, numerical methods can be used. As their name suggests, numerical methods use numerical calculations (i.e., numbers not symbols) to develop a unique solution to a differential equation. The solution is often in the form of a set of numbers, or a graph. This can then be used to analyze a particular design case. The solution is often returned quickly so that trial and error design techniques may be used. But, without a symbolic equation the system can be harder to understand and manipulate.

This chapter focuses on techniques that can be used for numerically integrating systems of differential equations.