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

^*Corresponding author for this work

Global Education Center

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

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) = -

Original language	English
Pages (from-to)	427-470
Number of pages	44
Journal	Japan Journal of Industrial and Applied Mathematics
Volume	33
Issue number	2
DOIs	https://doi.org/10.1007/s13160-016-0218-8
Publication status	Published - 2016 Jul 1

Keywords

Blow-up
Finite difference method
Nonlinear Schrödinger equation

ASJC Scopus subject areas

Engineering(all)
Applied Mathematics

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10.1007/s13160-016-0218-8

Cite this

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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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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

IS - 2

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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