English

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.

Keywords

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

R2 v1 2026-06-23T00:36:27.022Z