Finite difference scheme for two-dimensional periodic nonlinear Schrodinger equations
- 주제(키워드) Periodic nonlinear Schrodinger equation , Uniform Strichartz estimate , Continuum limit
- 주제(기타) Mathematics, Applied; Mathematics
- 설명문(일반) [Hong, Younghun] Chung Ang Univ, Dept Math, Seoul 06974, South Korea; [Kwak, Chulkwang] Ewha Womans Univ, Dept Math, Seoul 03760, South Korea; [Nakamura, Shohei] Tokyo Metropolitan Univ, Dept Math & Informat Sci, 1-1 Minami Ohsawa, Hachioji, Tokyo 1920397, Japan; [Yang, Changhun] Korea Inst Adv Study, Sch Math, Seoul 20455, South Korea; [Yang, Changhun] Jeonbuk Natl Univ, Inst Pure & Appl Math, Jeonju 54896, South Korea
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- OA유형 Green Submitted
- 발행기관 SPRINGER BASEL AG
- 발행년도 2021
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000183431
- 본문언어 영어
- Published As http://dx.doi.org/10.1007/s00028-020-00585-y
초록/요약
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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