One method consists in computing the numerical solution for an arbitrary and then . The Richardson extrapolation gives an estimate of of the error. When the error is smaller than the tolerance, we keep the result and start from . If the error is larger we restart with until we reach the tolerance.
( means approximation with )
I don't understand why the Richardson extrapolation is mentioned. For what do I have to use it? Can I not just calculate and and see the error?