is its numerical approximation depending on the step size h. Assume
we have the relation
where 
is an increasing sequence of positive numbers.
In each experiment, we will compute the numerical solution at each nodal
point with different step size h, let the sequence of the numerical
approximation at each node point be 
. Then we can compare the numerical solutions with the exact solution at
different nodal points. Afterwards, we can evaluate the ratio of two consecutive
errors, that is
From (5.2), we hope that this ratio will
tend to a certain number. Depending on the ratio, we can determine 
. The Richardson extrapolation technique is now used to increase the accuracy
of the numerical solutions. Denote 
, then for i=1 , we have
Repeat the same process, we can find the successive 
's and using the following general formula to find the more accurate approximations
Then we have
