High-order splitting integrators for nonlinear Schr\"odinger equations over long times
Numerical Analysis
2018-03-01 v1
Abstract
The long-time behaviour of splitting integrators applied to nonlinear Schr\"odinger equations in a weakly nonlinear setting is studied. It is proven that the energy is nearly conserved on long time intervals. The analysis includes all consistent splitting integrators with real-valued coefficients, in particular splitting integrators of high order. The proof is based on a completely resonant modulated Fourier expansion in time of the numerical solution.
Cite
@article{arxiv.1802.10324,
title = {High-order splitting integrators for nonlinear Schr\"odinger equations over long times},
author = {Ludwig Gauckler},
journal= {arXiv preprint arXiv:1802.10324},
year = {2018}
}
Comments
24 pages