FIXED POINT METHOD
Fixed Point
The idea behind the fixed point method is very simple: to find the solutions of a given nonlinear function
f(x) = 0, it is possible to rearrange f(x)= 0 into the form x = g(x), where g(x) denotes a function of x. Then, simply
start with an initial guess, x_{0} and apply the iteration process:
x_{n} = g(x_{n  1}) for n = 1,2,3,...

For example, to find solutions for the following nonlinear equation:
f(x) = sin x + e^{x} + x^{2}  2x = 0

There are several ways to rewrite the above equation into the form x = g(x). For example, it is possible to
rearrange the above equation into the following form:
x = 1/2(sin x + e^{x} + x^{2})

Or can be rearranged as:
