Simulation and Decay Prediction of Time-Fractional Dynamic Waves Evolution Based on Meshless Methods.
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| Title: | Simulation and Decay Prediction of Time-Fractional Dynamic Waves Evolution Based on Meshless Methods. |
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| Authors: | Zhao, RuI1 107552300623@stu.xju.edu.cn, Yang, Huanzhu1 596352335@qq.com, Sabir, Amina2 amina_sabir1@126.com, Imin, Rahmatjan3 rahmatjanim@xju.edu.cn |
| Source: | IAENG International Journal of Applied Mathematics. Jul2026, Vol. 56 Issue 7, p2405-2418. 14p. |
| Subjects: | Meshfree methods, Fractional calculus, Energy dissipation, Burgers' equation, Computer simulation |
| Abstract: | This paper presents, for the first time, a meshless scheme coupling the Symmetric Kernel Derivative Free Smoothed Particle Hydrodynamics (SKDF-SPH) method and L1 discretization for solving the time-fractional Burgers equation (TFBE), aiming to simulate dynamics wave evolution and predict decay. Specifically, the L1 method is employed to discretize the temporal Caputo derivative to capture the fractional "memory effect", while the SKDF-SPH handles spatial terms. This approach avoids computing kernel derivatives and can solve first-order and second-order derivatives, thus improving accuracy and efficiency in complex scenarios. Building on existing theoretical frameworks, this paper presents a proof of the decay theorem for time-fractional dynamic waves, clarifies the quantitative relationship between the norm decay characteristics of solutions and fractional orders, and validates them through three types of numerical examples. The examples with an analytical solutions demonstrates that the proposed method yields small errors in both 2 L and L norms, achieving a second-order convergence rate; the complex-boundary example without an analytical solution successfully captures the spatiotemporal coupled evolution law of dynamic waves; the long-term simulation of the homogeneous equation reveals the regulatory effect of the fractional order on decay -- a larger leads to more significant energy dissipation and diffusion. It is also determined that 4 serves as the optimal parameter for the decay rate, verifying the suboptimal decay property. The results demonstrates that this meshless scheme provides a reliable tool for simulating time-fractional dynamic waves and can be extended to related engineering fields. [ABSTRACT FROM AUTHOR] |
| Copyright of IAENG International Journal of Applied Mathematics is the property of International Association of Engineers (IAENG) 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 | Links: – Type: pdflink Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 195026873 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Simulation and Decay Prediction of Time-Fractional Dynamic Waves Evolution Based on Meshless Methods. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Zhao%2C+RuI%22">Zhao, RuI</searchLink><relatesTo>1</relatesTo><i> 107552300623@stu.xju.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Yang%2C+Huanzhu%22">Yang, Huanzhu</searchLink><relatesTo>1</relatesTo><i> 596352335@qq.com</i><br /><searchLink fieldCode="AR" term="%22Sabir%2C+Amina%22">Sabir, Amina</searchLink><relatesTo>2</relatesTo><i> amina_sabir1@126.com</i><br /><searchLink fieldCode="AR" term="%22Imin%2C+Rahmatjan%22">Imin, Rahmatjan</searchLink><relatesTo>3</relatesTo><i> rahmatjanim@xju.edu.cn</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22IAENG+International+Journal+of+Applied+Mathematics%22">IAENG International Journal of Applied Mathematics</searchLink>. Jul2026, Vol. 56 Issue 7, p2405-2418. 14p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Meshfree+methods%22">Meshfree methods</searchLink><br /><searchLink fieldCode="DE" term="%22Fractional+calculus%22">Fractional calculus</searchLink><br /><searchLink fieldCode="DE" term="%22Energy+dissipation%22">Energy dissipation</searchLink><br /><searchLink fieldCode="DE" term="%22Burgers'+equation%22">Burgers' equation</searchLink><br /><searchLink fieldCode="DE" term="%22Computer+simulation%22">Computer simulation</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This paper presents, for the first time, a meshless scheme coupling the Symmetric Kernel Derivative Free Smoothed Particle Hydrodynamics (SKDF-SPH) method and L1 discretization for solving the time-fractional Burgers equation (TFBE), aiming to simulate dynamics wave evolution and predict decay. Specifically, the L1 method is employed to discretize the temporal Caputo derivative to capture the fractional "memory effect", while the SKDF-SPH handles spatial terms. This approach avoids computing kernel derivatives and can solve first-order and second-order derivatives, thus improving accuracy and efficiency in complex scenarios. Building on existing theoretical frameworks, this paper presents a proof of the decay theorem for time-fractional dynamic waves, clarifies the quantitative relationship between the norm decay characteristics of solutions and fractional orders, and validates them through three types of numerical examples. The examples with an analytical solutions demonstrates that the proposed method yields small errors in both 2 L and L norms, achieving a second-order convergence rate; the complex-boundary example without an analytical solution successfully captures the spatiotemporal coupled evolution law of dynamic waves; the long-term simulation of the homogeneous equation reveals the regulatory effect of the fractional order on decay -- a larger leads to more significant energy dissipation and diffusion. It is also determined that 4 serves as the optimal parameter for the decay rate, verifying the suboptimal decay property. The results demonstrates that this meshless scheme provides a reliable tool for simulating time-fractional dynamic waves and can be extended to related engineering fields. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of IAENG International Journal of Applied Mathematics is the property of International Association of Engineers (IAENG) 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: Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 14 StartPage: 2405 Subjects: – SubjectFull: Meshfree methods Type: general – SubjectFull: Fractional calculus Type: general – SubjectFull: Energy dissipation Type: general – SubjectFull: Burgers' equation Type: general – SubjectFull: Computer simulation Type: general Titles: – TitleFull: Simulation and Decay Prediction of Time-Fractional Dynamic Waves Evolution Based on Meshless Methods. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Zhao, RuI – PersonEntity: Name: NameFull: Yang, Huanzhu – PersonEntity: Name: NameFull: Sabir, Amina – PersonEntity: Name: NameFull: Imin, Rahmatjan IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 07 Text: Jul2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 19929978 Numbering: – Type: volume Value: 56 – Type: issue Value: 7 Titles: – TitleFull: IAENG International Journal of Applied Mathematics Type: main |
| ResultId | 1 |
