Weak convergence of the Rosenbrock semi-implicit method for semilinear SPDEs
A talk in the SPDEvent series by
Jean Daniel Mukam from Uni Bielefeld
| Abstract: | Stochastic partial differential equations (SPDEs) are widely used to model many real world phenomena. Since explicit solutions of many SPDEs are unknown, numerical schemes are good alternative to provide their approximations. In this talk, we focus on semilinear SPDEs where the nonlinear component is more significant than the linear one (also called stiff problems). Rosenbrock-type methods have been shown to be efficient for such SPDEs. But only their strong convergence has been examined until now. We discuss the derivation of the Rosenbrock semi-implicit method and provide some ingredients useful for the proof of the weak convergence. The analysis does not use the Malliavin calculus, instead uses the Kolmogorov equation and the smoothing effects of the resolvent operator inherent in the Rosenbrock semi-implicit method. The rate of the weak convergence is twice that of the strong convergence. This is a join work with Antoine Tambue (Western Norway University of Applied Sciences). |