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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