Exploring computationally efficient stable numerical techniques for fractional Keller–Segel system modeling chemotaxis.
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| Title: | Exploring computationally efficient stable numerical techniques for fractional Keller–Segel system modeling chemotaxis. |
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| Authors: | Sagar, B1 (AUTHOR) b.sagar@ucf.edu, Saha Ray, S.1,2 (AUTHOR) santanusaharay@yahoo.com |
| Source: | Mathematics & Computers in Simulation. Jun2025, Vol. 232, p50-74. 25p. |
| Subjects: | Partition of unity method, Radial basis functions, Caputo fractional derivatives, Partition functions, Finite difference method, Meshfree methods |
| Abstract: | Chemotaxis is a biological phenomenon whereby unicellular organisms direct their movements in response to certain chemicals in their habitat. This study presents a numerical investigation of the fractional Keller–Segel model describing the aggregation of cellular slime molds and bacterial chemotaxis. Two numerical schemes are provided to solve this model; primarily, a meshfree numerical scheme based on the local radial basis function partition of unity method is presented. In this approach, the domain is split up into a number of smaller, overlapping subdomains, and the radial basis function interpolation is performed separately on each of these. On the other hand, a numerical method employing the L1 scheme for temporal discretization and centered difference for spatial discretization is introduced to compare the primary proposed method solutions with the simulations acquired by this method. Stability and convergence of the time-discrete algorithm are rigorously established. The strengths of the carried work is that the proposed approach is meshfree, where as the classical methods like finite difference/element approaches depends on mesh. Also, as per the best of authors knowledge, the analytical solutions of the considered fractional model are not known in literature, which makes the carried numerical investigation innovative. Computational experiments are carried out, and simulation results of both schemes are compared. Also, the density plots of cellular slime mold and the chemical attractant for specific biological parameters are illustrated to observe their biological behavior. [ABSTRACT FROM AUTHOR] |
| Copyright of Mathematics & Computers in Simulation 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 |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 183278113 AccessLevel: 6 PubType: Periodical PubTypeId: serialPeriodical PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Exploring computationally efficient stable numerical techniques for fractional Keller–Segel system modeling chemotaxis. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Sagar%2C+B%22">Sagar, B</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> b.sagar@ucf.edu</i><br /><searchLink fieldCode="AR" term="%22Saha+Ray%2C+S%2E%22">Saha Ray, S.</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> santanusaharay@yahoo.com</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Mathematics+%26+Computers+in+Simulation%22">Mathematics & Computers in Simulation</searchLink>. Jun2025, Vol. 232, p50-74. 25p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Partition+of+unity+method%22">Partition of unity method</searchLink><br /><searchLink fieldCode="DE" term="%22Radial+basis+functions%22">Radial basis functions</searchLink><br /><searchLink fieldCode="DE" term="%22Caputo+fractional+derivatives%22">Caputo fractional derivatives</searchLink><br /><searchLink fieldCode="DE" term="%22Partition+functions%22">Partition functions</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+difference+method%22">Finite difference method</searchLink><br /><searchLink fieldCode="DE" term="%22Meshfree+methods%22">Meshfree methods</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Chemotaxis is a biological phenomenon whereby unicellular organisms direct their movements in response to certain chemicals in their habitat. This study presents a numerical investigation of the fractional Keller–Segel model describing the aggregation of cellular slime molds and bacterial chemotaxis. Two numerical schemes are provided to solve this model; primarily, a meshfree numerical scheme based on the local radial basis function partition of unity method is presented. In this approach, the domain is split up into a number of smaller, overlapping subdomains, and the radial basis function interpolation is performed separately on each of these. On the other hand, a numerical method employing the L1 scheme for temporal discretization and centered difference for spatial discretization is introduced to compare the primary proposed method solutions with the simulations acquired by this method. Stability and convergence of the time-discrete algorithm are rigorously established. The strengths of the carried work is that the proposed approach is meshfree, where as the classical methods like finite difference/element approaches depends on mesh. Also, as per the best of authors knowledge, the analytical solutions of the considered fractional model are not known in literature, which makes the carried numerical investigation innovative. Computational experiments are carried out, and simulation results of both schemes are compared. Also, the density plots of cellular slime mold and the chemical attractant for specific biological parameters are illustrated to observe their biological behavior. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Mathematics & Computers in Simulation 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.matcom.2024.12.011 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 25 StartPage: 50 Subjects: – SubjectFull: Partition of unity method Type: general – SubjectFull: Radial basis functions Type: general – SubjectFull: Caputo fractional derivatives Type: general – SubjectFull: Partition functions Type: general – SubjectFull: Finite difference method Type: general – SubjectFull: Meshfree methods Type: general Titles: – TitleFull: Exploring computationally efficient stable numerical techniques for fractional Keller–Segel system modeling chemotaxis. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Sagar, B – PersonEntity: Name: NameFull: Saha Ray, S. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 06 Text: Jun2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 03784754 Numbering: – Type: volume Value: 232 Titles: – TitleFull: Mathematics & Computers in Simulation Type: main |
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