One should be careful not to read too much into the results shown in the above example. The optimum ranges for h and N depend on the differential equation, the numerical method that is used, and the number of digits that are retained in the calculation. Nevertheless, it is generally true that if too many steps are required in a calculation, then eventually round-off error is likely to accumulate to the point that it seriously degrades the accuracy of the procedure. For many problems this is not a concern: for them any of the fourth order methods we have discussed earlier will produce good results with a number of steps far less than the level at which round-off error becomes important. For some problems, however, round-off error does becomes vitally important. For such problems the choice of method may be crucial. This is also one reason why modern codes provide a means of adjusting the step size as they go along, using a larger step size wherever possible, and a very small step size only where necessary.