Fourier spectral methods based on restricted Padé approximations for space fractional reaction-diffusion systems.
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| Title: | Fourier spectral methods based on restricted Padé approximations for space fractional reaction-diffusion systems. |
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| Authors: | Yousuf, M.1 (AUTHOR) myousuf@kfupm.edu.sa, Alshayqi, M.1 (AUTHOR) munirah.shayqi@kfupm.edu.sa, Alzahrani, S.S.2 (AUTHOR) sszahrani@taibahu.edu.sa |
| Source: | Computers & Mathematics with Applications. Mar2025, Vol. 181, p228-247. 20p. |
| Subjects: | Matrix exponential, Neumann boundary conditions, Discrete cosine transforms, Laplacian matrices, Transfer matrix |
| Abstract: | By utilizing the power of the Fourier spectral approach and the restricted Padé rational approximations, we have devised two third-order numerical methods to investigate the complex phenomena that arise in multi-dimensional space fractional reaction-diffusion models. The Fourier spectral approach yields a fully diagonal representation of the fractional Laplacian with the ability to extend the methods to multi-dimensional cases with the same computational complexity as one-dimensional and makes it possible to attain spectral convergence. Third-order single-pole restricted Padé approximations of the matrix exponential are utilized in developing the time stepping methods. We also use sophisticated mathematical techniques, namely, discrete sine and cosine transforms, to improve the computational efficiency of the methods. Algorithms are derived from these methods for straight-forward implementation in one- and multidimensional models, accommodating both homogeneous Dirichlet and homogeneous Neumann boundary conditions. The third-order accuracy of these methods is proved analytically and demonstrated numerically. Linear error analysis of these methods is presented, stability regions of both methods are computed, and their graphs are plotted. The computational efficiency, reliability, and effectiveness of the presented methods are demonstrated through numerical experiments. The convergence results are computed to support the theoretical findings. [ABSTRACT FROM AUTHOR] |
| Copyright of Computers & Mathematics with Applications is the property of Pergamon Press - An Imprint of Elsevier Science 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: 183035362 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Fourier spectral methods based on restricted Padé approximations for space fractional reaction-diffusion systems. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Yousuf%2C+M%2E%22">Yousuf, M.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> myousuf@kfupm.edu.sa</i><br /><searchLink fieldCode="AR" term="%22Alshayqi%2C+M%2E%22">Alshayqi, M.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> munirah.shayqi@kfupm.edu.sa</i><br /><searchLink fieldCode="AR" term="%22Alzahrani%2C+S%2ES%2E%22">Alzahrani, S.S.</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> sszahrani@taibahu.edu.sa</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Computers+%26+Mathematics+with+Applications%22">Computers & Mathematics with Applications</searchLink>. Mar2025, Vol. 181, p228-247. 20p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Matrix+exponential%22">Matrix exponential</searchLink><br /><searchLink fieldCode="DE" term="%22Neumann+boundary+conditions%22">Neumann boundary conditions</searchLink><br /><searchLink fieldCode="DE" term="%22Discrete+cosine+transforms%22">Discrete cosine transforms</searchLink><br /><searchLink fieldCode="DE" term="%22Laplacian+matrices%22">Laplacian matrices</searchLink><br /><searchLink fieldCode="DE" term="%22Transfer+matrix%22">Transfer matrix</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: By utilizing the power of the Fourier spectral approach and the restricted Padé rational approximations, we have devised two third-order numerical methods to investigate the complex phenomena that arise in multi-dimensional space fractional reaction-diffusion models. The Fourier spectral approach yields a fully diagonal representation of the fractional Laplacian with the ability to extend the methods to multi-dimensional cases with the same computational complexity as one-dimensional and makes it possible to attain spectral convergence. Third-order single-pole restricted Padé approximations of the matrix exponential are utilized in developing the time stepping methods. We also use sophisticated mathematical techniques, namely, discrete sine and cosine transforms, to improve the computational efficiency of the methods. Algorithms are derived from these methods for straight-forward implementation in one- and multidimensional models, accommodating both homogeneous Dirichlet and homogeneous Neumann boundary conditions. The third-order accuracy of these methods is proved analytically and demonstrated numerically. Linear error analysis of these methods is presented, stability regions of both methods are computed, and their graphs are plotted. The computational efficiency, reliability, and effectiveness of the presented methods are demonstrated through numerical experiments. The convergence results are computed to support the theoretical findings. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Computers & Mathematics with Applications is the property of Pergamon Press - An Imprint of Elsevier Science 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.camwa.2024.12.025 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 20 StartPage: 228 Subjects: – SubjectFull: Matrix exponential Type: general – SubjectFull: Neumann boundary conditions Type: general – SubjectFull: Discrete cosine transforms Type: general – SubjectFull: Laplacian matrices Type: general – SubjectFull: Transfer matrix Type: general Titles: – TitleFull: Fourier spectral methods based on restricted Padé approximations for space fractional reaction-diffusion systems. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Yousuf, M. – PersonEntity: Name: NameFull: Alshayqi, M. – PersonEntity: Name: NameFull: Alzahrani, S.S. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 03 Text: Mar2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 08981221 Numbering: – Type: volume Value: 181 Titles: – TitleFull: Computers & Mathematics with Applications Type: main |
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