The computational efficiency of RK methods can be improved if the step size is allowed to vary during a simulation. A reasonable criterion must be established for determining when it is appropriate to modify the step size and by how much. The criterion is usually based on an estimate of the local truncation error as the simulation progresses with time. If an estimate of the local truncation error is outside an acceptable tolerance, then it is possible to either reduce the step size when the estimated error is too large or quite possibly increase the step size if it appears that the error is unnecessarily small. Techniques for estimating the local truncation error and modifying the step size, if warranted, are referred to ...
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