Time Splitting and Error Estimates for Nonlinear Schrödinger Equations with a Potential

IF 2.7 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Foundations of Computational Mathematics Pub Date : 2025-08-12 DOI:10.1007/s10208-025-09727-5

Rémi Carles

引用次数: 0

Abstract

We consider the nonlinear Schrödinger equation with a potential, also known as Gross-Pitaevskii equation. By introducing a suitable spectral localization, we prove low regularity error estimates for the time discretization corresponding to an adapted Lie-Trotter splitting scheme. The proof is based on tools from spectral theory and pseudodifferential calculus in order to obtain various estimates on the spectral localization, including discrete Strichartz estimates which support the nonlinear analysis.

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带电位非线性Schrödinger方程的时间分裂和误差估计

我们考虑具有势的非线性Schrödinger方程，也称为Gross-Pitaevskii方程。通过引入合适的光谱定位，我们证明了时间离散化的低规则误差估计对应于自适应的Lie-Trotter分裂方案。利用谱理论和伪微分学的工具进行了证明，得到了谱局部化的各种估计，包括支持非线性分析的离散Strichartz估计。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Foundations of Computational Mathematics 数学-计算机：理论方法

CiteScore

6.90

自引率

3.30%

发文量

审稿时长

>12 weeks

期刊介绍： Foundations of Computational Mathematics (FoCM) will publish research and survey papers of the highest quality which further the understanding of the connections between mathematics and computation. The journal aims to promote the exploration of all fundamental issues underlying the creative tension among mathematics, computer science and application areas unencumbered by any external criteria such as the pressure for applications. The journal will thus serve an increasingly important and applicable area of mathematics. The journal hopes to further the understanding of the deep relationships between mathematical theory: analysis, topology, geometry and algebra, and the computational processes as they are evolving in tandem with the modern computer. With its distinguished editorial board selecting papers of the highest quality and interest from the international community, FoCM hopes to influence both mathematics and computation. Relevance to applications will not constitute a requirement for the publication of articles. The journal does not accept code for review however authors who have code/data related to the submission should include a weblink to the repository where the data/code is stored.