Stefan Hilger's time scale calculus is commonly known for unifying the corresponding theories of ordinary differential and difference equations, but has been designed to tackle problems in Numerical Analysis right from the beginning.
In this talk, we aim to illustrate that time scales provide a convenient framework for variable stepsize discretizations of ordinary differential equations: Using an abstract perturbation result for dynamic equations on time scales, we show that stability properties and integral manifolds of nonautonomous differential equations persist under numerical one-step schemes, and one has convergence with order of the method. This illustrates a further application of time scales beyond the often mentioned unification aspect.
S. Keller and C. Pötzsche. Integral manifolds under explicit variable time-step discretization. J. Difference Equ. Appl., 12(3–4), 321–342, 2005.
Wykładowca: prof. Christian Pötzsche, Alpen-Adria Universität Klagenfurt, Austria