Kinetic equations and numerical approximation of solutions (Tino Laidin)

Interacting particle systems appear in many areas of physics and biology. The models we are interested in range from gas dynamics to semiconductors to chemotaxis.
These systems can be classified into three main scales: particle (microscopic), kinetic (mesoscopic) and fluid (macroscopic). This presentation will focus on the kinetic description. In this context, the unknown is the particle distribution function which is a solution of a partial differential equation.
In general, PDEs are difficult to solve analytically and sometimes no explicit solution is available. By discretising the problem, a numerical method can be designed to approximate the solution. In this talk, the finite difference method will be presented and illustrated by several simulations.