Maximum norm error estimates of fourth-order compact difference scheme for the nonlinear Schrödinger equation involving a quintic term

A compact finite difference (CFD) scheme is presented for the nonlinear Schrödinger equation involving a quintic term. The two discrete conservative laws are obtained. The unconditional stability and convergence in maximum norm with order [Formula: see text] are proved by using the energy method. A ...

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Detalles Bibliográficos
Autores principales: Hu, Hanqing, Hu, Hanzhang
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2018
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6061535/
https://www.ncbi.nlm.nih.gov/pubmed/30137908
http://dx.doi.org/10.1186/s13660-018-1775-y
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author Hu, Hanqing
Hu, Hanzhang
author_facet Hu, Hanqing
Hu, Hanzhang
author_sort Hu, Hanqing
collection PubMed
description A compact finite difference (CFD) scheme is presented for the nonlinear Schrödinger equation involving a quintic term. The two discrete conservative laws are obtained. The unconditional stability and convergence in maximum norm with order [Formula: see text] are proved by using the energy method. A numerical experiment is presented to support our theoretical results.
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spelling pubmed-60615352018-08-09 Maximum norm error estimates of fourth-order compact difference scheme for the nonlinear Schrödinger equation involving a quintic term Hu, Hanqing Hu, Hanzhang J Inequal Appl Research A compact finite difference (CFD) scheme is presented for the nonlinear Schrödinger equation involving a quintic term. The two discrete conservative laws are obtained. The unconditional stability and convergence in maximum norm with order [Formula: see text] are proved by using the energy method. A numerical experiment is presented to support our theoretical results. Springer International Publishing 2018-07-20 2018 /pmc/articles/PMC6061535/ /pubmed/30137908 http://dx.doi.org/10.1186/s13660-018-1775-y Text en © The Author(s) 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Hu, Hanqing
Hu, Hanzhang
Maximum norm error estimates of fourth-order compact difference scheme for the nonlinear Schrödinger equation involving a quintic term
title Maximum norm error estimates of fourth-order compact difference scheme for the nonlinear Schrödinger equation involving a quintic term
title_full Maximum norm error estimates of fourth-order compact difference scheme for the nonlinear Schrödinger equation involving a quintic term
title_fullStr Maximum norm error estimates of fourth-order compact difference scheme for the nonlinear Schrödinger equation involving a quintic term
title_full_unstemmed Maximum norm error estimates of fourth-order compact difference scheme for the nonlinear Schrödinger equation involving a quintic term
title_short Maximum norm error estimates of fourth-order compact difference scheme for the nonlinear Schrödinger equation involving a quintic term
title_sort maximum norm error estimates of fourth-order compact difference scheme for the nonlinear schrödinger equation involving a quintic term
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6061535/
https://www.ncbi.nlm.nih.gov/pubmed/30137908
http://dx.doi.org/10.1186/s13660-018-1775-y
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