Unconditional optimal-order error estimates of linear relaxation compact difference scheme for the coupled nonlinear Schrödinger system.
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| Title: | Unconditional optimal-order error estimates of linear relaxation compact difference scheme for the coupled nonlinear Schrödinger system. |
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| Authors: | Gao, Ying1 (AUTHOR) gy9168@stu.ouc.edu.cn, Fu, Hongfei1,2 (AUTHOR) fhf@ouc.edu.cn, Wang, Xiaoying1 (AUTHOR) wxy7121@stu.ouc.edu.cn |
| Source: | Applied Numerical Mathematics. Sep2026, Vol. 227, p108-128. 21p. |
| Subjects: | Nonlinear Schrödinger equation, Error analysis in mathematics, Conservation of energy, Algorithms, Finite difference method, Relaxation methods (Mathematics), Conservation of mass |
| Abstract: | This paper presents a linear, decoupled, mass- and energy-conserving numerical scheme for the multi-dimensional coupled nonlinear Schrödinger (CNLS) system. The scheme combines the fourth-order compact difference approximation in space with the relaxation technique in a time-staggered mesh framework, enabling the sequential solution of the primal unknowns and the introduced auxiliary relaxation variables with high efficiency and high-order accuracy. We establish the unique solvability and discrete conservation laws of the proposed scheme. In particular, for the first time, by leveraging an auxiliary error equation system together with a cut-off technique, optimal-order error estimates are rigorously proved–without any coupling mesh conditions–for the primal variables in the discrete H 1-norm at the time nodes, and for the auxiliary relaxation variables in the discrete L 2-norm at the intermediate time nodes. This constitutes the primary theoretical contribution of this paper for multi-dimensional CNLS system. Numerical experiments demonstrate convincingly the strong performance of the proposed scheme in long-term simulations, maintaining both physical invariants and high-order accuracy. [ABSTRACT FROM AUTHOR] |
| Copyright of Applied Numerical Mathematics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Header | DbId: egs DbLabel: Engineering Source An: 194123926 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Unconditional optimal-order error estimates of linear relaxation compact difference scheme for the coupled nonlinear Schrödinger system. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Gao%2C+Ying%22">Gao, Ying</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> gy9168@stu.ouc.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Fu%2C+Hongfei%22">Fu, Hongfei</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> fhf@ouc.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Wang%2C+Xiaoying%22">Wang, Xiaoying</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> wxy7121@stu.ouc.edu.cn</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Applied+Numerical+Mathematics%22">Applied Numerical Mathematics</searchLink>. Sep2026, Vol. 227, p108-128. 21p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Nonlinear+Schrödinger+equation%22">Nonlinear Schrödinger equation</searchLink><br /><searchLink fieldCode="DE" term="%22Error+analysis+in+mathematics%22">Error analysis in mathematics</searchLink><br /><searchLink fieldCode="DE" term="%22Conservation+of+energy%22">Conservation of energy</searchLink><br /><searchLink fieldCode="DE" term="%22Algorithms%22">Algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+difference+method%22">Finite difference method</searchLink><br /><searchLink fieldCode="DE" term="%22Relaxation+methods+%28Mathematics%29%22">Relaxation methods (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Conservation+of+mass%22">Conservation of mass</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This paper presents a linear, decoupled, mass- and energy-conserving numerical scheme for the multi-dimensional coupled nonlinear Schrödinger (CNLS) system. The scheme combines the fourth-order compact difference approximation in space with the relaxation technique in a time-staggered mesh framework, enabling the sequential solution of the primal unknowns and the introduced auxiliary relaxation variables with high efficiency and high-order accuracy. We establish the unique solvability and discrete conservation laws of the proposed scheme. In particular, for the first time, by leveraging an auxiliary error equation system together with a cut-off technique, optimal-order error estimates are rigorously proved–without any coupling mesh conditions–for the primal variables in the discrete H 1-norm at the time nodes, and for the auxiliary relaxation variables in the discrete L 2-norm at the intermediate time nodes. This constitutes the primary theoretical contribution of this paper for multi-dimensional CNLS system. Numerical experiments demonstrate convincingly the strong performance of the proposed scheme in long-term simulations, maintaining both physical invariants and high-order accuracy. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Applied Numerical Mathematics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.apnum.2026.04.011 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 21 StartPage: 108 Subjects: – SubjectFull: Nonlinear Schrödinger equation Type: general – SubjectFull: Error analysis in mathematics Type: general – SubjectFull: Conservation of energy Type: general – SubjectFull: Algorithms Type: general – SubjectFull: Finite difference method Type: general – SubjectFull: Relaxation methods (Mathematics) Type: general – SubjectFull: Conservation of mass Type: general Titles: – TitleFull: Unconditional optimal-order error estimates of linear relaxation compact difference scheme for the coupled nonlinear Schrödinger system. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Gao, Ying – PersonEntity: Name: NameFull: Fu, Hongfei – PersonEntity: Name: NameFull: Wang, Xiaoying IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 09 Text: Sep2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 01689274 Numbering: – Type: volume Value: 227 Titles: – TitleFull: Applied Numerical Mathematics Type: main |
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