Miller Hederi, University of Central Florida


Efficiency of numerical solution methods to the nonlinear Schroedinger equations

Abstract: In optics and wave mechanics, nonlinear equations arise and exhibit important phenomena, such as rogue waves. Because of this, fast and accurate nonlinear numerical techniques are needed so these phenomena may be further analyzed. In our research, we compare the efficiency of existing split-step and exponential time differencing methods on the nonlinear Schroedinger equation as well as develop an adaptive step-size control algorithm for the exponential time differencing method. We test the performance of the various methods with soliton initial data. In numerical experiments we compare the analytical solution to the numerical as well as track the conservation of mass and energy. Numerical simulations show that the exponential time differencing method performs approximately ten times faster than the more widely used split-step scheme, while the adaptive techniques' performances fall short of their non-adaptive counterparts.

Mentors: Dr. A. L. Islas and Dr. C. M. Schober (University of Central Florida).

Collaborator: Kyle S. Reger (University of Central Florida).