Simulating stochastic inertial manifolds by a backward-forward approach (Q2871335)

The authors deal with an inertial manifold of a stochastic evolutionary equation with multiplicative noise. Based on a theory of Da Prato and Debussche the stochastic evolutionary system is divided into a forward and a backward part, i.e. a coupled backward-forward system. The backward part is finite dimensional and the forward part is infinite dimensional. Then, the coupled system is discretized in space by a Picard iteration. In addition, the iteration is also discretized in time where the conditional expectation is involved in the backward part (due to the need of an adapted solution) and an Euler scheme is used for the forward part. After establishing the convergence of the numerical scheme the authors show the existence of an approximated inertial manifold. Finally, two examples are given where the obtained numerical scheme is applied: The first example deals with a system of stochastic ordinary differential equations, the second one with a stochastic partial differential equation.