A priori error analysis of linear and nonlinear periodic Schr{\"o}dinger equations with analytic potentials
Numerical Analysis
2023-12-21 v2 Numerical Analysis
Abstract
This paper is concerned with the numerical analysis of linear and nonlinear Schr{\"o}dinger equations with analytic potentials. While the regularity of the potential (and the source term when there is one) automatically conveys to the solution in the linear cases, this is no longer true in general in the nonlinear case. We also study the rate of convergence of the planewave (Fourier) discretization method for computing numerical approximations of the solution.
Keywords
Cite
@article{arxiv.2206.04954,
title = {A priori error analysis of linear and nonlinear periodic Schr{\"o}dinger equations with analytic potentials},
author = {Eric Cancès and Gaspard Kemlin and Antoine Levitt},
journal= {arXiv preprint arXiv:2206.04954},
year = {2023}
}