ABSTRACT
In Chapter 3 it was shown that the task of finding the length of a wave in water of
variable depth or normal depth in an open channel could be cast as a particular
class of problem: that of finding the roots of an equation. Mathematically this can
be expressed as finding x such that f(x) = 0. This type of problem often arises in
situations where the solution must be determined over and over again and some sort
of numerical technique is generally required. The combination of modern
computers and numerical techniques provides a powerful engineering tool. One
numerical technique that is particularly well suited to this type of problem is based
on starting with two guesses for the root, one larger, the other smaller than the
actual value, and then gradually refining these until a suitable solution is reached.
This is known as a bracket method and is widely applied in engineering.
