A Two-Step Numerical Scheme in Time for Surface Quasi Geostrophic Equations Under Location Uncertainty - Fiorini, Camilla; Boulvard, Pierre-Marie; Li, Long; Mémin, Etienne (Stochastic Transport in Upper Ocean Dynamics)
Abstract In this work we consider the surface quasi-geostrophic (SQG) system under location uncertainty (LU) and propose a Milstein-type scheme for these equations, which is then used in a multi-step method. The SQG system considered here consists of one stochastic partial differential equation, which models the stochastic transport of the buoyancy, and a linear operator linking the velocity and the buoyancy. In the LU setting, the Euler-Maruyama scheme converges with weak order 1 and strong order 0.5. Our aim is to develop higher order schemes in time, based on a Milstein-type scheme in a multi-step framework. First we compared different kinds of Milstein schemes. The scheme with the best performance is then included in the two-step scheme. Finally, we show how our two-step scheme decreases the error in comparison to other multi-step schemes.
DOI: 10.1007/978-3-031-18988-3_5
Keywords: bookSection