On the dynamics of high-speed current collection systems described by differential equations II.
- Speaker: Martin Buhmann, Justus-Liebig University Giessen (Germany).
- Virtual room: https://meet.google.com/bcs-iujv-auh
- Dates: November 25 (Monday), 11:30-12:30 and November 27 (Wednesday), 12:30-13:30.
Abstract:
The numerical analysis and computation of solutions of differential equations is always at the very centre of applied mathematics and approximation theory. Both boundary value problems (cf., e.g., B., Jódar and Rodríguez, 2019) and initial value problems need approximations by splines, polynomials, quasi-interpolants, radial basis functions etc. (see, e.g., B. and Jäger, 2022) of the local solutions for the algorithms to work efficiently.
A particularly fascinating special case of initial value problems is the situation of delay equation where the solution of the equations depends also on the past and not only on the current values of the solutions. The dynamics of these solutions are naturally much more difficult (non-linear) but there are interesting railway engineering applications which we shall discuss: namely, the current collecting systems of modern high-speed trains (AVE, Eurostar) from overhead wires supported in intervals by stiff springs can be reliably described by delay differential equations. We shall discuss the current situation of research and future challenges in different lectures.