[PDE&A] Paul Zegeling: A generalized midpoint-based BV-method for unstable PDEs (and beyond)

16 mei 2024 16:00 t/m 17:00 - Locatie: Lipkenszaal 36.LB01.150 | Zet in mijn agenda

We will discuss a generalized midpoint-based boundary-value method and its application to unstable and ill-posed partial differential equations (PDEs). Furthermore, an extension of this technique to DE systems with periodic
solutions, e.g., the harmonic oscillator and predator-prey equations will be proposed.

Boundary-value methods (BVMs) are generalizations of traditional time-integrators such as linear multistep or Runge-Kutta methods. They make use of additional final and, if appropriate, extra initial conditions as well.

The generalized midpoint-based BMV has the special property that its stability region is the whole complex plane (excluding the imaginary axis). This opens interesting new application areas (compared to the well-known and widely-accepted time-integration techniques): the backward heat equation and similar ill-posed or unstable PDEs. Examples will be given for several models in this class. In addition, replacing the final conditions in the BVM by periodic conditions, we can apply this approach to DEs with periodic solution behaviour. Especially, it is interesting to investigate models with center points, limit cycles and where the conservation of energy in Hamiltonian DE systems plays a role.