WG5 - Numerical methods and applications
Since the differential equations which arise in applications like cell cycle, biological resource and demographic models, or vehicular traffic on road networks have a rather complicated structure, the analytical approach to the analysis of the dynamics of the corresponding system is not viable. Hence numerical methods are highly important for the success of the project.
The present project aims at finding most suitable numerical methods for applications appearing in the working plans of WG1-4. To this end, the existing approximation results will be analysed, and new techniques will be developed by taking into account the special requirements of modelling on networks.
The list of applications which will be tackled includes wave propagation in pipeline and road networks, dynamics of chemical networks, geodetic networks and multi-physics system simulations. These applications have important ramifications in real life and the development of successful numerical methods for them would be highly beneficial to the industrial partners.
- Determine the spatial differential operator in problems proposed by WG2 and WG3, and provide appropriate space discretization techniques.
- Develop numerical methods specially designed for problems proposed by WG2 and WG3.
- Use the semigroup approach, and especially the results of WG1 and WG4, to prove the convergence of the new numerical methods.
- Generalize the results to broader classes of problems in network modelling.
- Apply the developed numerical methods to the applications proposed by the industrial partners.