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An introduction to Volterra integral equations on time scales
by
Tomasia Kulik
School of Mathematics and Statistics, University of New South Wales
Coauthors: Christopher C. Tisdell (School of Mathematics and Statistics, University of New South Wales)
"Time scales theory" studies differential equations and difference equations under one unifying framework, and so is able to advance, as special cases, both the theory of differential equations and the theory of difference equations. Moreover, dynamic equations on time scales can accurately model the more complex hybrid system or process where the dynamics vary continuously part of the time and vary discretely for part of the time. These hybrid continuous-discrete time dynamics processes occur in both physical systems (electronic circuits) and biological systems (population dynamics, ecosystems) and are most accurately modelled by dynamic equations on time scales.
I will present new theoretical results on the existence and uniqueness of solutions and numerical methods for finding the solution of Volterra integral equations on time scales, as well as the applications of these equations to modelling complex systems. The research utilises fixed point theory, including Banach's fixed point theorem and Granas's continuation theorem for contractions.
Date received: February 14, 2008
Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caws-33.