Finite difference scheme for two-dimensional periodic nonlinear Schrodinger equations

被引：5

作者：

Hong, Younghun ^{[1
]}

Kwak, Chulkwang ^{[2
]}

Nakamura, Shohei ^{[3
]}

Yang, Changhun ^{[4
,5
]}

机构：

[1] Chung Ang Univ, Dept Math, Seoul 06974, South Korea

[2] Ewha Womans Univ, Dept Math, Seoul 03760, South Korea

[3] Tokyo Metropolitan Univ, Dept Math & Informat Sci, 1-1 Minami Ohsawa, Hachioji, Tokyo 1920397, Japan

[4] Korea Inst Adv Study, Sch Math, Seoul 20455, South Korea

[5] Jeonbuk Natl Univ, Inst Pure & Appl Math, Jeonju 54896, South Korea

来源：

JOURNAL OF EVOLUTION EQUATIONS | 2021年 / 21卷 / 01期

基金：

新加坡国家研究基金会;

关键词：

Periodic nonlinear Schrodinger equation; Uniform Strichartz estimate; Continuum limit; DISPERSIVE PROPERTIES; CONVERGENCE; DERIVATION;

D O I：

10.1007/s00028-020-00585-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A nonlinear Schrodinger equation (NLS) on a periodic box can be discretized as a discrete nonlinear Schrodinger equation (DNLS) on a periodic cubic lattice, which is a system of finitely many ordinary differential equations. We show that in two spatial dimensions, solutions to the DNLS converge strongly in L-2 to those of the NLS as the grid size h > 0 approaches zero. As a result, the effectiveness of the finite difference method (FDM) is justified for the two-dimensional periodic NLS.

引用

页码：391 / 418

页数：28

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