|Institutional Office Address
DMIF, Room NS2, Phone: +39 0432 558401
|Research Project Title
Applications of High Performance Computing to models in the field of biomathematics
|Research Project Description
I am studying numerical methods for the investigation of the dynamical and bifurcation properties of particular mathematical models in the fields of biomathematics, such as ecology and population dynamics.
Some implementations of such methods exist already (e.g. in the Matlab environment) but typically require too much of computational time when applied to realistic models. I am, in particular, trying to develop alternative and efficient implementations of numerical continuation and methods to compute periodic solutions.
Recently, discretization methods are proposed to reduce delay differential equations coupled with renewal equations to systems of ordinary differential equations (ODEs). These techniques are particularly useful to treat complex models describing structured populations, where rates like fertility or survival probability depend on external ODEs, which in turns change with model parameters. Continuation tools are then applied to analyze stability and detect bifurcations. My research is based on the idea that taking somehow advantage of the structure of the problem – i.e., of solutions to the external ODEs computed for previous values of the parameters – is likely to improve the overall performance. To this aim, I am currently working on a prototype problem where the solution of an external ODE, through standard collocation, is included in the continuation framework rather than being obtained externally from scratch.