+ = = + = +

From this example, it is obvious that the stable step size is controlled by the rapid transient associated with the exponential term. At large times, that transient has completely died out and the solution is dominated totally by the asymptotic large time solution, yet) = t + 2. If an accurate small time solution is required, then the small step size required for stability may be larger than the small step size required for accuracy. In that case, explicit methods can be used. However, if the early transient solution is of no interest, and an accurate large time solution is required, explicit methods are unsuitable because of the small stable step size.