Numerical methods for differential equations
Karátson, János (working group leader); Faragó, István; Fekete, Imre; Hadjimichael, Yiannis; Havasi, Ágnes; Horváth, Róbert; Izsák, Ferenc; Kalmár-Nagy, Tamás; Kovács, Balázs; Mincsovics, Miklós; Sebestyén, Gabriella
Discrete mathematics and graph theory
Katona, Gyula Y. (working group leader); Kunszenti-Kovács, Dávid; Papp, László; Lovász, László
Network processes and differential equations
Several processes such as epidemic spread, activity in neuronal networks or rumour spreading can be described by stochastic processes on graphs. The master equations are systems of linear ODEs, the size of which is exponentially large in terms of the number of nodes in the graph. Hence different nonlinear ODE approximations have been developed for different graphs. The validity of these approximations is investigated by using dynamical system methods. The research is extended to adaptive networks and to controlling the process by changing the structure of the graph.Simon, Péter (working group leader); Bodó, Ágnes; Katona, Gyula Y.; Nagy, Noémi
Operator semigroups for shallow water equations
Shallow water equations represent a special case of Navier-Stokes equations for incompressible and inviscid fluids moving on the rotating Earth as first proposed by Saint-Venant in 1871. They played an important role in the first attempts to describe the atmosphere's large-scale dynamics. Since numerical weather prediction models and ocean dynamical models, e.g. tsunami forecasting, are still based on shallow water-like equations, their effective numerical treatment is an important issue. Our research concentrates on the application of innovative time integrators, such as operator splitting procedures, exponential integrators, and Magnus intergators, for shallow water equations.Csomós, Petra (working group leader); Faragó, István; Farkas, Rita; Havasi, Ágnes