In order to assess the accuracy of numerical integration,
and possibly adjust the *stepsize* so as to maintain
the requested accuracy employ *step doubling*:

- 1.
- take the step twice
- (a)
- once as a full step, leading to
- (b)
- then as two half steps, leading to

- 2.
- Estimate the truncation error by

- 3.
- Return as an answer, because that's going to be the more accurate one.
- 4.
- Since
assuming that we try two different values of
we should have:

This yields the following formula for a step size:

**Strategy**- Let
be the
*requested*accuracy.