Finite difference approximation for nonlinear Schrödinger equations with application to blow-up computation

Norikazu Saito; Takiko Sasaki

doi:10.1007/s13160-016-0218-8

Finite difference approximation for nonlinear Schrödinger equations with application to blow-up computation

Norikazu Saito^*, Takiko Sasaki

^*この研究の対応する著者

グローバルエデュケーションセンター

研究成果: Article › 査読

4 被引用数 (Scopus)

抄録

This paper presents a coherent analysis of the finite difference method to nonlinear Schrödinger (NLS) equations in one spatial dimension. We use the discrete H¹ framework to establish well-posedness and error estimates in the L^∞ norm. The nonlinearity f(u) of a NLS equation is assumed to satisfy only a growth condition. We apply our results to computation of blow-up solutions for a NLS equation with the nonlinearity f(u) = -

本文言語	English
ページ（範囲）	427-470
ページ数	44
ジャーナル	Japan Journal of Industrial and Applied Mathematics
巻	33
号	2
DOI	https://doi.org/10.1007/s13160-016-0218-8
出版ステータス	Published - 2016 7月 1

ASJC Scopus subject areas

工学（全般）
応用数学

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10.1007/s13160-016-0218-8

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abstract = "This paper presents a coherent analysis of the finite difference method to nonlinear Schr{\"o}dinger (NLS) equations in one spatial dimension. We use the discrete H1 framework to establish well-posedness and error estimates in the L∞ norm. The nonlinearity f(u) of a NLS equation is assumed to satisfy only a growth condition. We apply our results to computation of blow-up solutions for a NLS equation with the nonlinearity f(u) = -",

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author = "Norikazu Saito and Takiko Sasaki",

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AU - Sasaki, Takiko

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N2 - This paper presents a coherent analysis of the finite difference method to nonlinear Schrödinger (NLS) equations in one spatial dimension. We use the discrete H1 framework to establish well-posedness and error estimates in the L∞ norm. The nonlinearity f(u) of a NLS equation is assumed to satisfy only a growth condition. We apply our results to computation of blow-up solutions for a NLS equation with the nonlinearity f(u) = -

AB - This paper presents a coherent analysis of the finite difference method to nonlinear Schrödinger (NLS) equations in one spatial dimension. We use the discrete H1 framework to establish well-posedness and error estimates in the L∞ norm. The nonlinearity f(u) of a NLS equation is assumed to satisfy only a growth condition. We apply our results to computation of blow-up solutions for a NLS equation with the nonlinearity f(u) = -

KW - Blow-up

KW - Finite difference method

KW - Nonlinear Schrödinger equation

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JO - Japan Journal of Industrial and Applied Mathematics

JF - Japan Journal of Industrial and Applied Mathematics

SN - 0916-7005

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Finite difference approximation for nonlinear Schrödinger equations with application to blow-up computation

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