@Article{NMTMA-1-198,
author = {Qin Sheng},
title = {A Paradoxical Consistency Between Dynamic and Conventional Derivatives on Hybrid Grids},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2008},
volume = {1},
number = {2},
pages = {198--213},
abstract = {<p style="text-align: justify;">It has been evident that the theory and methods of dynamic
derivatives are playing an increasingly important rôle in hybrid
modeling and computations. Being constructed on various kinds of
hybrid grids, that is, time scales, dynamic derivatives offer
superior accuracy and flexibility in approximating mathematically
important natural processes with hard-to-predict singularities, such
as the epidemic growth with unpredictable jump sizes and option
market changes with high uncertainties, as compared with
conventional derivatives. In this article, we shall review the novel
new concepts, explore delicate relations between the most frequently
used second-order dynamic derivatives and conventional derivatives.
We shall investigate necessary conditions for guaranteeing the
consistency between the two derivatives. We will show that such a
consistency may never exist in general. This implies that the
dynamic derivatives provide entirely different new tools for
sensitive modeling and approximations on hybrid grids. Rigorous
error analysis will be given via asymptotic expansions for further
modeling and computational applications. Numerical experiments will
also be given.</p>},
issn = {2079-7338},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/nmtma/6048.html}
}