Basic Calculus on Time Scales and Some of Its Applications
Abstract
The study of dynamic systems on time scales not only unifies continuous and discrete processes, but also helps in revealing diversities in the corresponding results. In this paper we shall develop basic tools of calculus on time scales such as versions of Taylor's formula, l'Hôspital's rule, and Kneser's theorem. Applications of these results in the study of asymptotic and oscillatory behavior of solutions of higher order equations on time scales are addressed. As a further application of Taylor's formula, Abel-Gontscharoff interpolating polynomial on time scales is constructed and best possible error bounds are offered. We have also included notes at the end of each section which indicate further scope of the calculus developed in this paper.
Recommended Citation
M. Bohner and R. P. Agarwal, "Basic Calculus on Time Scales and Some of Its Applications," Results in Mathematics, Springer Verlag, Jan 1999.
The definitive version is available at https://doi.org/10.1007/BF03322019
Department(s)
Mathematics and Statistics
Keywords and Phrases
time scales; Taylor's theorem; l'Hôspital's rule; kneeser's Theorem; Abel-Gontscharoff interpolation
International Standard Serial Number (ISSN)
1422-6383
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 1999 Springer Verlag, All rights reserved.
Publication Date
01 Jan 1999
