Schwerin, R. von. private correspondence, University of Heidelberg (1993). Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Experiments in stepsize control for Adams linear multistep methods - Willé (2000) (Correct)
....of suitable orders and stepsizes is non trivial and has been the subject of much research. Given suitable methods to compute and advance the integration formulae, it can make the difference between a good and a bad code. A number of different approaches have been suggested for this problem [1, 2, 4, 5, 8, 9, 10, 11]. This work concentrates on and extends two of these: one implemented by Shampine in his code RDEAM [11] and a second, simpler, version based on the difference between a predictor and corrector formula. Communicated by Prof. C. T. H. Baker, this document originally appeared as an IWR preprint ....
....By retaining the notation and the variables of schemes used to advance the integration, the broader mathematical context is lost. The dependence of h is spread in a complicated way throughout several terms and extensive manipulation and assumptions are needed to make even the smallest advances [1, 4, 9]. Confronted with this problem, it is natural to take one step back. Recurrence relations (c.f. for g k 1;1 and g k;1 ) rescaling ratios (fi k 1 ) and heuristics are clearly important for the practical implementation of numerical codes but distract from the basic principles underlying their ....
[Article contains additional citation context not shown here]
Schwerin, R. von. private correspondence, University of Heidelberg (1993).
Experiments in stepsize control for Adams linear multistep methods - Wille (1994) (Correct)
....of suitable orders and stepsizes is non trivial and has been the subject of much research. Given suitable methods to compute and advance the integration formulae, it can make the difference between a good and a bad code. A number of different approaches have been suggested for this problem [1, 2, 4, 5, 8, 9, 10, 11]. This work concentrates on and extends two of these: one implemented by Shampine in his code RDEAM [11] and a second, simpler, version based on the difference between a predictor and corrector formula. Communicated by Prof. C. T. H. Baker, this document originally appeared as an IWR preprint ....
....By retaining the notation and the variables of schemes used to advance the integration, the broader mathematical context is lost. The dependence of h is spread in a complicated way throughout several terms and extensive manipulation and assumptions are needed to make even the smallest advances [1, 4, 9]. Confronted with this problem, it is natural to take one step back. Recurrence relations (c.f. for g k 1;1 and g k;1 ) rescaling ratios (fi k 1 ) and heuristics are clearly important for the practical implementation of numerical codes but distract from the basic principles underlying their ....
[Article contains additional citation context not shown here]
Schwerin, R. von. private correspondence, University of Heidelberg (1993).
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