Thu, 07 Oct 2010
11:00
11:00
DH 3rd floor SR
In this talk we describe a general framework for deriving
modified equations for stochastic differential equations with respect to
weak convergence. We will start by quickly recapping of how to derive
modified equations in the case of ODEs and describe how these ideas can
be generalized in the case of SDEs. Results will be presented for first
order methods such as the Euler-Maruyama and the Milstein method. In the
case of linear SDEs, using the Gaussianity of the underlying solutions,
we will derive a SDE that the numerical method solves exactly in the
weak sense. Applications of modified equations in the numerical study
of Langevin equations and in the calculation of effective diffusivities
will also be discussed.