##
The Trapezoidal Method with linear iterations

Let's consider the model problem

dy/dt = -20*y

y(0) = 1

0 <= t <= 2

A simple script to solve this with linear iterations
can be **downloaded here **.
Again, it uses the functions
**deriv.m ** and
**exact.m **.
We know that the solution of this problem decays, and that in fact

y(t) = exp(-20*t)

Let's look at results where the first guess for w(i+1) is obtained with
Euler's method. In the following 2 graphs, we first 0 iterations, and then
iterations until w(i+1)^(j) is within a certain tolerance of w(i+1)^(j-1).

Without Iterations:

With Iterations: