Numerical analysis and simulation of PDEs with random dispersion
Numerous complex mathematical models in science and engineering are subject to random fluctuations and other uncertainties. These random terms and uncertainties come from, for instance, errors in the measurement of input variables, random environmental fluctuations, errors due to simplifying model assumptions, or errors/unknowns in the model parameters. Such random terms and uncertainties are often described as stochastic processes in the mathematical models resulting in stochastic (partial) differential equations.
In this project, we are particularly interested in eminent stochastic partial differential equations in modern communication systems (the stochastic Schrödinger equation with white noise dispersion and the Manakov equation). Such equations are often termed as partial differential equations with random dispersion. Due to the complexity of these problems, it is impossible to find a solution by traditional means (paper and pencil). One must resort to numerical simulations. There is therefore a demand for efficient and reliable numerical methods for the approximation of solutions to these stochastic partial differential equations.The results of this project will lead to the development and analysis of efficient numerical methods for efficient approximations and simulations of solutions to partial differential equations with random dispersion.