Numerical integration for time scales
Ettinger, Bree danielle
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Time Scale theory unifies and extends real and discrete analysis. Euler’s Method is an algorithm for constructing a linear approximation to the initial value problem dy/dt = f(t, y) a < t < b and y(a) = a . Although Euler’s Method is seldom used in practice, it lays the ground work for developing higher order approximation schemes. In this thesis, we use Euler’s Method to develop a numerical integration scheme for time scales. First we explore our numerical integration scheme on an isolated time scale, and then extend our results to an arbitrary time scale. We also give error approximations for these schemes as well as examples.