Hybrid approximations via second order combined dynamic derivatives on time scales
This article focuses on the approximation of conventional second order derivative via the combined (diamond-$\alpha$) dynamic derivative on time scales with necessary smoothness conditions embedded. We will show the constraints under which the second order dynamic derivative provides a consistent ap...
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| Format: | Article |
| Language: | English |
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University of Szeged
2007-09-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=275 |
| Summary: | This article focuses on the approximation of conventional second order derivative via the combined (diamond-$\alpha$) dynamic derivative on time scales with necessary smoothness conditions embedded. We will show the constraints under which the second order dynamic derivative provides a consistent approximation to the conventional second derivative; the cases where the dynamic derivative approximates the derivative only via a proper modification of the existing formula; and the situations in which the dynamic derivative can never approximate consistently even with the help of available structure correction methods. Constructive error analysis will be given via asymptotic expansions for practical hybrid modeling and computational applications. |
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| ISSN: | 1417-3875 1417-3875 |