The numerical unified transform method for the nonlinear Schrödinger equation on the half-line

We implement the numerical unified transform method to solve nonlinear Schrödinger equation on half-line. For so-called linearizable boundary conditions, solves half-line problems with comparable complexity as inverse scattering whole-line problems. In particular, computes solution at any x and t without spatial discretization or time stepping. Contour deformations based of steepest descent are used so that method’s computational cost does not increase for large , is more accurate increase. Our ideas also apply some cases where conditions linearizable.