Numerical Integrators for Continuous Disordered Nonlinear Schrodinger Equation

In this paper, we consider the numerical solution of the continuous disordered nonlinear Schrodinger equation, which contains a spatial random potential. We address the finite time accuracy order reduction issue of the usual numerical integrators on this problem, which is due to the presence of the random/rough potential. By using the recently proposed lowregularity integrator (LRI) from (33, SIAM J Numer Anal, 2019), we show how to integrate the potential term by losing two spatial derivatives. Convergence analysis is done to showthat LRI has the second order accuracy in L-2-norm for potentials in H-2. Numerical experiments are done to verify this theoretical result. More numerical results are presented to investigate the accuracy of LRI compared with classical methods under rougher random potentials from applications.