Explicit numerical methods for the time discretisation of stochastic wave equations
In this project we are particularly interested in stochastic wave equations describing, for example, electromagnetic or acoustic waves subject to random forces.
Numerous complex dynamical systems are subject to random fluctuations and other uncertainties. These uncertainties are often described as stochastic terms in the models resulting in stochastic differential equations. In this project we are particularly interested in stochastic wave equations describing, for example, electromagnetic or acoustic waves subject to random forces. A concrete example may be given by an equation describing the motion of a strand of DNA floating in a liquid. Here, the random force acting on the strand of DNA comes from the particles of the liquid hitting the DNA randomly. Due to the complexity of these problems, it is impossible to find a solution by traditional means (paper, pencil) and we must resort to a numerical solution. In addition to the above DNA problem, many other important applications are also modeled by such stochastic partial differential equations: the motion of a suspended cable under wind loading; the motion of shock waves on the surface of the sun; or the motion of a nonlinear stochastic beam. There is therefore a demand for efficient and reliable numerical methods for the approximation of solutions to these problems. The results of this project will lead to the development and analysis of efficient numerical methods for the numerical solution of stochastic wave equations. The proposal asks mainly for the funding of one PhD student.