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.
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页码：391 / 418
页数：28
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