On Optimal Convergence Rates for the Nonlinear Schr\"{o}dinger Equation with a Wave Operator via Localized Orthogonal Decomposition
Numerical Analysis
2026-03-24 v1 Numerical Analysis
Computational Physics
Abstract
In this paper, we develop a Localized Orthogonal Decomposition (LOD) method for the two-dimensional time-dependent nonlinear Schr\"{o}dinger equation with a wave operator. We prove that our method preserves conservation laws and admits a unique numerical solution; furthermore, we obtain unconditional (i.e., time-step restriction-free) optimal-order superconvergent error estimates. To complement the theoretical analysis, we present a series of numerical simulations that verify the analytical results and further illustrate structural aspects of the problem.
Keywords
Cite
@article{arxiv.2603.20627,
title = {On Optimal Convergence Rates for the Nonlinear Schr\"{o}dinger Equation with a Wave Operator via Localized Orthogonal Decomposition},
author = {Hanzhang Hu and Zetao Ma and Lei Zhang},
journal= {arXiv preprint arXiv:2603.20627},
year = {2026}
}