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math.NA2016
Convergence of a Normalized Gradient Algorithm for Computing Ground States
Erwan Faou, Tiphaine Jézéquel
We consider the approximation of the ground state of the one-dimensional cubic nonlinear Schr{ö}dinger equation by a normalized gradient algorithm combined with linearly implicit t…
math.NA2013
Resonant time steps and instabilities in the numerical integration of Schrödinger equations
Erwan Faou, Tiphaine Jézéquel
We consider the linear and non linear cubic Schrödinger equations with periodic boundary conditions, and their approximations by splitting methods. We prove that for a dense set of…