Dynamic equations and applications
Makaleler > Tam Makale · 2006
Yazarlar: Martin Bohner, Allan Peterson
Advances in Difference Equations, Uluslararası, Scopus, 2006, cilt 2006, ss 1-2
Özet
Going back to its founder Stefan Hilger (1988), the study of dynamic equations on time scales is a fairly new area of mathematics. Motivating the subject is the notion that dynamic equations on time scales can build bridges between continuous and discrete mathematics. Time is considered to be an element of an arbitrary closed subset of the reals, the so-called time scale. Dynamic equations on the time scale of all real numbers are differential equations, while dynamic equations on the time scale of all integers are difference equations. But not only is this theory able to unify the continuous and the discrete, it also can help to extend these theories to cases "in between" and to other dynamic equations (e.g., q-difference equations). The study of time scales theory has led to several important applications, for example, in the study of insect population models, neural networks, heat transfer, quantum mechanics, and epidemic models.