PUB - Publikationen an der Universität Bielefeld

We consider the nonlinear Schrodinger equation with dispersion modulated by a (formal) derivative of a time-dependent function with fractional Sobolev regularity of class W-alpha,W-2 for some alpha is an element of (0, 1). Due to the loss of smoothness in the problem, classical numerical methods face severe order reduction. In this work, we develop and analyze a new randomized exponential integrator based on a stratifiedMonte Carlo approximation. The new discretization technique averages the high oscillations in the solution allowing for improved convergence rates of order alpha + 1/2. In addition, the new approach allows us to treat a far more general class of modulations than the available literature. Numerical results underline our theoretical findings and show the favorable error behavior of our new scheme compared to classical methods.