Low Regularity Full Error Estimates for the Cubic Nonlinear Schrödinger Equation

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Numerical Analysis Pub Date : 2024-09-03 DOI:10.1137/23m1619617

Lun Ji, Alexander Ostermann, Frédéric Rousset, Katharina Schratz

引用次数: 0

Abstract

SIAM Journal on Numerical Analysis, Volume 62, Issue 5, Page 2071-2086, October 2024.
Abstract. For the numerical solution of the cubic nonlinear Schrödinger equation with periodic boundary conditions, a pseudospectral method in space combined with a filtered Lie splitting scheme in time is considered. This scheme is shown to converge even for initial data with very low regularity. In particular, for data in [math], where [math], convergence of order [math] is proved in [math]. Here [math] denotes the time step size and [math] the number of Fourier modes considered. The proof of this result is carried out in an abstract framework of discrete Bourgain spaces; the final convergence result, however, is given in [math]. The stated convergence behavior is illustrated by several numerical examples.

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立方非线性薛定谔方程的低正则全误差估计

SIAM 数值分析期刊》，第 62 卷，第 5 期，第 2071-2086 页，2024 年 10 月。摘要。对于具有周期性边界条件的立方非线性薛定谔方程的数值求解，考虑了空间伪谱法与时间滤波列分裂方案相结合的方法。结果表明，即使初始数据的规律性很低，该方案也能收敛。特别是，对于[math]中的数据，其中[math]，[math]中证明了阶[math]的收敛性。这里 [math] 表示时间步长，[math] 表示考虑的傅立叶模式数。这一结果的证明是在离散布尔干空间的抽象框架中进行的；而最终的收敛结果则在 [math] 中给出。所述收敛行为通过几个数值示例加以说明。

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

SIAM Journal on Numerical Analysis 数学-应用数学

CiteScore

4.80

自引率

6.90%

发文量

110

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Numerical Analysis (SINUM) contains research articles on the development and analysis of numerical methods. Topics include the rigorous study of convergence of algorithms, their accuracy, their stability, and their computational complexity. Also included are results in mathematical analysis that contribute to algorithm analysis, and computational results that demonstrate algorithm behavior and applicability.