Claudine von Hallern: On the Numerical Approximation of Stochastic Partial Differential Equations

Abstract

Stochastic partial differential equations are a powerful tool in modeling various phenomena from finance to the ocean sciences. Since analytical solutions to these equations are, in general,not computable, there is a high demand for numerical schemes to approximate these processes. In this talk,we give a short introduction to stochastic partial differential equations and illustrate the characteristics of numerical schemes for this type of equation. The solution process belongs to a Hilbert space of infinite dimension, so the approximation requires a discretization in space and time and an approximation of the driving stochastic process. We focus on derivative-free methods that maintain the same high order of convergence compared to schemes that include the derivative of the diffusion operator but at the same time involve a reduced computational cost.