Example 4.  Determine how much the solutions in example 2 and 3 differ.

Solution 4.

We cannot merely form the difference between the solutions, because they do not have the same dimension.  

We will need to extract every other point from points2 and make a list which contains the same length as points1.

    Does the error look small? Large? Can it be improved?

    We now use Richardson's improvement scheme and extrapolate the seemingly inaccurate solutions in examples 2 and 3.

We should discover the joy of understanding the order of a numerical method.  

(c) John H. Mathews 2003