Conveners
Geometric numerical integration of S(P)DEs
- Raffaele D'Ambrosio (University of L'Aquila)
Description
This talk explores the interplay between geometric numerical integration and stochastic numerical methods. The focus is on recent advances in the design and analysis of numerical schemes that preserve qualitative and quantitative properties, as well as invariance laws, governing the dynamics of stochastic ordinary and partial differential equations.
The presentation is organized around two main themes. The first concerns geometric numerical integration for stochastic Hamiltonian systems. Two distinct settings are considered: when the noise is interpreted in the Itô sense, the expected value of the Hamiltonian exhibits a linear drift in time, whereas in the Stratonovich setting the Hamiltonian is preserved pathwise. For both cases, the behavior of selected numerical methods with respect to the preservation of these properties is discussed, together with a long-time analysis based on backward error analysis. The second theme addresses structure-preserving numerical methods for dissipative stochastic problems. In particular, the numerical preservation of mean-square contractivity in the time integration of dissipative systems is investigated using stochastic theta-methods. The analysis reveals that mean-square contractivity at the discrete level is ensured under suitable stepsize restrictions.
A unifying perspective is provided by establishing a conceptual bridge between the numerical treatment of stochastic problems and that of their underlying deterministic counterparts.
This talk is based on joint work with H. Biscevic (GSSI), Chuchu Chen (Chinese Academy of Sciences), David Cohen (Chalmers University of Technology & University of Gothenburg), Stefano Di Giovacchino (University of L’Aquila), and Annika Lang (Chalmers University of Technology & University of Gothenburg).
