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Section: New Results

Exponential integrators for nonlinear Schrödinger equations with white noise dispersion

Together with D. Cohen, G. Dujardin has proposed several exponential numerical methods for the time integration of the nonlinear Schrödinger equation with power law nonlinearity and random dispersion [11]. In particular, he introduced a new explicit exponential integrator for this purpose that integrates the noisy part of the equation exactly. He prove that this scheme is of mean-square order 1 and he drew consequences of this fact. He compared the exponential integrator with several other numerical methods from the literature. Finally, he proposed a second exponential integrator, which is implicit and symmetric and, in contrast to the first one, preserves the ${L}^{2}$−norm of the solution.