## 2012 Young Researchers Workshop:Kinetic Description of Multiscale Phenomena

### Uniform error estimates of numerical methods for NLSW

Yongyong Cai

We propose an exponential wave integrator sine pseudospectral (EWI-SP) method for the nonlinear Schr"{o}dinger equation (NLS) with wave operator (NLSW), and carry out rigorous error analysis. NLSW is NLS perturbed by the wave operator with strength described by a dimensionless parameter $varepsilonin(0,1]$. As $varepsilon o0^+$, NLSW converges to NLS and for the small perturbation, i.e. \$0