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
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).