Open boundary conditions and computational schemes for Schrödinger equations with general potentials and nonlinearities

Christophe Besse (Université Lille 1, France)

This talk will address the construction of absorbing boundary conditions for the one-dimensional Schrödinger equation with a general variable repulsive potential or with a cubic nonlinearity. Semi-discrete time schemes, based on Crank-Nicolson approximations, will be presented for the associated initial boundary value problems. Finally, some numerical simulations will give a comparison of the various absorbing boundary conditions to analyse their accuracy and efficiency.