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Order and stepsize control in extrapolation methods. (English) Zbl 0543.65049
This paper presents a new theory for joint order and stepsize control in extrapolation methods which is based on measuring the discretization errors by the subdiagonal rather than diagonal entries of the extrapolation tableau. An optimal column index, which defines a locally optimal order, is chosen by minimizing the work per unit step over all columns up to some maximum column index. In addition Shannon’s information theory is applied to derive a convergence model that is expected to describe the behaviour of an extrapolation method on a large set of test problems. Some numerical testing indicates an improvement in efficiency and robustness for this new device.
Reviewer: K.Burrage

65L05 Numerical methods for initial value problems
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