Ekvationer
Seminarium i matematik

Numerical approximation of the stochastic wave equation and its covariance

Välkommen till föreläsningen i seminarieserien i matematik.

In this talk, we give an introduction to the stochastic wave equation, which is a fundamental stochastic PDE (SPDE). Restricting ourselves to the linear case, we use the mild Itô formula to obtain an operator-valued integral equation for the covariance of this SPDE. We explain how both the SPDE and the associated integral equation can be approximately solved using finite elements and rational approximations of the wave equation semigroup. Convergence rates are obtained that are seen to be sharp in numerical simulations.