Section: New Results

Numerical methods for evolution equations

In [36] G. Dujardin analyzes an exponential integrator applied to the nonlinear Schrödinger equation with white noise dispersion. This models appears in optic fibers. Together with his co-author, he proves that this explicit scheme applied to the sctochastic PDE is of mean-square order 1. He uses it to illustrate a conjecture on the well-posedness of the equation in some regimes of the nonlinearity. Comparisons with several other schemes of the litterature are proposed. A last, another new (implicit) exponential integrators is proposed, which preserves the $L^2$-norm of the solution and is compared with the explicit one introduced beforehand.