Computational and Applied Mathematics seminar

Abstract:Backward error analysis is a powerful tool in order to capture the long-term behaviour of numerical integrators. In this talk, we address our attention on providing a backward error analysis (both in the strong and weak sense) for classes of numerical methods. From one hand, the attention will be devoted to symplectic methods and Poisson integrators for stochastic Hamiltonian and Poisson systems. Here, we present strategies for deriving stochastic modified equations for the aforementioned integrators and we study them for obtaining long-term estimates on the Hamiltonian errors along the numerical dynamics. From the other hand, the weak backward error approach will be developed towards stochastic optimization algorithms, with the aim of gaining insights of their behaviour. This talk is based on joint researches with Raffaele D'Ambrosio (University of L'Aquila), Desmond J. Higham and Konstantios C. Zygalakis (University of Edinburgh).