Approximately Solutions of the Generalized Regular Long Wave Equation Utilizing Four Different Operator Splitting Algorithms Combined with the Finite Element Method.

Λεπτομέρειες βιβλιογραφικής εγγραφής
Τίτλος:	Approximately Solutions of the Generalized Regular Long Wave Equation Utilizing Four Different Operator Splitting Algorithms Combined with the Finite Element Method.
Συγγραφείς:	Karta, Melike
Πηγή:	Communications Series A1 Mathematics & Statistics; 2026, Vol. 75 Issue 2, p331-349, 19p
Θεματικοί όροι:	Finite element method, Algorithms, Galerkin methods, Partial differential equations, Spline theory, Numerical analysis
Περίληψη:	The one-dimensional nonlinear generalized regular wave GRLW equation with physical boundary conditions will be taken into consideration in this article. This study employs operator splitting algorithms in together with the finite element based Galerkin method, which is a practical and highly adaptable method for the approximately solution of the equation. The study's goal is to generate more precise and appealing results. B-splines serve as the foundation for the application of Galerkin methods in this study. Four distinct numerical schemes are utilized for the numerical results obtained throughout the article: Lie-Trotter splitting techniques LΔt = P-M,LΔt = M-P and Strang splitting techniques SΔt = P-M-P,SΔt = M-P-M and itisevaluated which of these methods yields the most accurate results. The work take into consideration the algorithm's output that yields the best results. Using the suggested techniques, the study has been put into practice to solve the single solitary wave and the interaction of two solitary waves problems. Error norms have been calculated in this article, and the newly acquired results are compared with those discovered by some researchers in the literature to show the precision and appeal of the numerical techniques employed. Furthermore, The current method is indicated to be unconditionally stable through the use of the Von-Neumann analysis. This study, which will be carried out after the literature review, will create a new and more effective solution method for the (GRLW) equation. [ABSTRACT FROM AUTHOR]
	Copyright of Communications Series A1 Mathematics & Statistics is the property of Ankara University 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.)
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Items	– Name: Title Label: Title Group: Ti Data: Approximately Solutions of the Generalized Regular Long Wave Equation Utilizing Four Different Operator Splitting Algorithms Combined with the Finite Element Method. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Karta%2C+Melike%22">Karta, Melike</searchLink> – Name: TitleSource Label: Source Group: Src Data: Communications Series A1 Mathematics & Statistics; 2026, Vol. 75 Issue 2, p331-349, 19p – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Finite+element+method%22">Finite element method</searchLink><br /><searchLink fieldCode="DE" term="%22Algorithms%22">Algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Galerkin+methods%22">Galerkin methods</searchLink><br /><searchLink fieldCode="DE" term="%22Partial+differential+equations%22">Partial differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Spline+theory%22">Spline theory</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: The one-dimensional nonlinear generalized regular wave GRLW equation with physical boundary conditions will be taken into consideration in this article. This study employs operator splitting algorithms in together with the finite element based Galerkin method, which is a practical and highly adaptable method for the approximately solution of the equation. The study's goal is to generate more precise and appealing results. B-splines serve as the foundation for the application of Galerkin methods in this study. Four distinct numerical schemes are utilized for the numerical results obtained throughout the article: Lie-Trotter splitting techniques L<subscript>Δt</subscript> = P-M,L<subscript>Δt</subscript> = M-P and Strang splitting techniques S<subscript>Δt</subscript> = P-M-P,S<subscript>Δt</subscript> = M-P-M and itisevaluated which of these methods yields the most accurate results. The work take into consideration the algorithm's output that yields the best results. Using the suggested techniques, the study has been put into practice to solve the single solitary wave and the interaction of two solitary waves problems. Error norms have been calculated in this article, and the newly acquired results are compared with those discovered by some researchers in the literature to show the precision and appeal of the numerical techniques employed. Furthermore, The current method is indicated to be unconditionally stable through the use of the Von-Neumann analysis. This study, which will be carried out after the literature review, will create a new and more effective solution method for the (GRLW) equation. [ABSTRACT FROM AUTHOR] – Name: Abstract Label: Group: Ab Data: <i>Copyright of Communications Series A1 Mathematics & Statistics is the property of Ankara University 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: 10.31801/cfsuasmas.1691496 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 19 StartPage: 331 Subjects: – SubjectFull: Finite element method Type: general – SubjectFull: Algorithms Type: general – SubjectFull: Galerkin methods Type: general – SubjectFull: Partial differential equations Type: general – SubjectFull: Spline theory Type: general – SubjectFull: Numerical analysis Type: general Titles: – TitleFull: Approximately Solutions of the Generalized Regular Long Wave Equation Utilizing Four Different Operator Splitting Algorithms Combined with the Finite Element Method. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Karta, Melike IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 04 Text: 2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 13035991 Numbering: – Type: volume Value: 75 – Type: issue Value: 2 Titles: – TitleFull: Communications Series A1 Mathematics & Statistics Type: main
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