Mapped Legendre collocation methods for linear Volterra-Fredholm integral equations with delays on a semi-infinite interval.
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| Title: | Mapped Legendre collocation methods for linear Volterra-Fredholm integral equations with delays on a semi-infinite interval. |
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| Authors: | Boutarcha, Sofiane1, Rahmoune, Azedine2 azedine.rahmoune@univ-setif.dz, Guechi, Ahmed3 |
| Source: | Mathematical Modelling & Analysis. 2026, Vol. 31 Issue 3, p499-520. 22p. |
| Subjects: | Integral equations, Volterra equations, Orthogonal functions, Numerical solutions to integral equations, Numerical analysis, Gaussian quadrature formulas |
| Abstract: | In this paper, we present a collocation method for linear Volterra-Fredholm integral equations with delay on a semi-infinite interval. The method employs orthogonal mapped Legendre basis functions together with a mapped Gauss quadrature rule adapted to the Volterra operator, leading to a stable and well-conditioned linear system. The convergence properties of both the collocation and iterated collocation solutions are investigated in the L2- and L8-norms, and algebraic convergence rates are derived under mild regularity assumptions. Several numerical examples are presented and discussed to show the accuracy and efficiency of the methods. [ABSTRACT FROM AUTHOR] |
| Copyright of Mathematical Modelling & Analysis is the property of Vilnius Gediminas Technical 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.) | |
| Database: | Engineering Source |
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| Header | DbId: egs DbLabel: Engineering Source An: 194823835 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Mapped Legendre collocation methods for linear Volterra-Fredholm integral equations with delays on a semi-infinite interval. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Boutarcha%2C+Sofiane%22">Boutarcha, Sofiane</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Rahmoune%2C+Azedine%22">Rahmoune, Azedine</searchLink><relatesTo>2</relatesTo><i> azedine.rahmoune@univ-setif.dz</i><br /><searchLink fieldCode="AR" term="%22Guechi%2C+Ahmed%22">Guechi, Ahmed</searchLink><relatesTo>3</relatesTo> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Mathematical+Modelling+%26+Analysis%22">Mathematical Modelling & Analysis</searchLink>. 2026, Vol. 31 Issue 3, p499-520. 22p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Integral+equations%22">Integral equations</searchLink><br /><searchLink fieldCode="DE" term="%22Volterra+equations%22">Volterra equations</searchLink><br /><searchLink fieldCode="DE" term="%22Orthogonal+functions%22">Orthogonal functions</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+solutions+to+integral+equations%22">Numerical solutions to integral equations</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Gaussian+quadrature+formulas%22">Gaussian quadrature formulas</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In this paper, we present a collocation method for linear Volterra-Fredholm integral equations with delay on a semi-infinite interval. The method employs orthogonal mapped Legendre basis functions together with a mapped Gauss quadrature rule adapted to the Volterra operator, leading to a stable and well-conditioned linear system. The convergence properties of both the collocation and iterated collocation solutions are investigated in the L2- and L8-norms, and algebraic convergence rates are derived under mild regularity assumptions. Several numerical examples are presented and discussed to show the accuracy and efficiency of the methods. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Mathematical Modelling & Analysis is the property of Vilnius Gediminas Technical 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: 10.3846/mma.2026.24076 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 22 StartPage: 499 Subjects: – SubjectFull: Integral equations Type: general – SubjectFull: Volterra equations Type: general – SubjectFull: Orthogonal functions Type: general – SubjectFull: Numerical solutions to integral equations Type: general – SubjectFull: Numerical analysis Type: general – SubjectFull: Gaussian quadrature formulas Type: general Titles: – TitleFull: Mapped Legendre collocation methods for linear Volterra-Fredholm integral equations with delays on a semi-infinite interval. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Boutarcha, Sofiane – PersonEntity: Name: NameFull: Rahmoune, Azedine – PersonEntity: Name: NameFull: Guechi, Ahmed IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 07 Text: 2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 13926292 Numbering: – Type: volume Value: 31 – Type: issue Value: 3 Titles: – TitleFull: Mathematical Modelling & Analysis Type: main |
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