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A localized radial basis function-based approach for quenching phenomenon of two-dimensional semilinear wave equation.

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Title: A localized radial basis function-based approach for quenching phenomenon of two-dimensional semilinear wave equation.
Authors: Singh, Shreya1 (AUTHOR) shreyasingh.rs.mat23@itbhu.ac.in, Burman, Riya Kumari1 (AUTHOR) riyakumariburman.rs.mat22@itbhu.ac.in, Pandey, Rajesh K.1 (AUTHOR) rkpandey.mat@iitbhu.ac.in, Xu, Yufeng2 (AUTHOR) xuyufeng@csu.edu.cn
Source: International Journal of Numerical Methods for Heat & Fluid Flow. 2026, Vol. 36 Issue 5, p1825-1856. 32p.
Subjects: Radial basis functions, Nonlinear wave equations, Finite difference method, Stability theory, Numerical analysis, Microelectromechanical systems, Energy function
Abstract: Purpose: Semilinear wave equations with different source terms describe acoustic wave motion in fluids, shock wave formation that decelerates fluid from supersonic to subsonic speeds and quenching phenomena in micro-electro mechanical systems devices with fluid mechanical applications. This paper aims to investigate the quenching behavior of numerical solutions for a two-dimensional semilinear wave equation with an inverse power law term. Design/methodology/approach: The localized radial basis function-generated finite difference (RBF-FD) method is used for approximating numerical solutions in space, and the finite difference scheme is used for temporal discretization. A discrete energy analysis is conducted to evaluate the local stability of the developed numerical scheme. Findings: The energy functional of the classical solution is defined. The numerical results demonstrate finite-time quenching, and the influence of various parameters is assessed through detailed numerical simulation. Originality/value: An RBF-FD approach is applied to confront the quenching phenomena in one- and two-dimensional cases. Stability and the computational performance of the proposed numerical scheme are verified numerically. The impact of various parameters and domains on quenching time is studied in detail. [ABSTRACT FROM AUTHOR]
Copyright of International Journal of Numerical Methods for Heat & Fluid Flow is the property of Emerald Publishing Limited 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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DbLabel: Engineering Source
An: 193119255
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Items – Name: Title
  Label: Title
  Group: Ti
  Data: A localized radial basis function-based approach for quenching phenomenon of two-dimensional semilinear wave equation.
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Singh%2C+Shreya%22">Singh, Shreya</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> shreyasingh.rs.mat23@itbhu.ac.in</i><br /><searchLink fieldCode="AR" term="%22Burman%2C+Riya+Kumari%22">Burman, Riya Kumari</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> riyakumariburman.rs.mat22@itbhu.ac.in</i><br /><searchLink fieldCode="AR" term="%22Pandey%2C+Rajesh+K%2E%22">Pandey, Rajesh K.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> rkpandey.mat@iitbhu.ac.in</i><br /><searchLink fieldCode="AR" term="%22Xu%2C+Yufeng%22">Xu, Yufeng</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> xuyufeng@csu.edu.cn</i>
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  Label: Source
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  Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Numerical+Methods+for+Heat+%26+Fluid+Flow%22">International Journal of Numerical Methods for Heat & Fluid Flow</searchLink>. 2026, Vol. 36 Issue 5, p1825-1856. 32p.
– Name: Subject
  Label: Subjects
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Radial+basis+functions%22">Radial basis functions</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+wave+equations%22">Nonlinear wave equations</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+difference+method%22">Finite difference method</searchLink><br /><searchLink fieldCode="DE" term="%22Stability+theory%22">Stability theory</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Microelectromechanical+systems%22">Microelectromechanical systems</searchLink><br /><searchLink fieldCode="DE" term="%22Energy+function%22">Energy function</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Purpose: Semilinear wave equations with different source terms describe acoustic wave motion in fluids, shock wave formation that decelerates fluid from supersonic to subsonic speeds and quenching phenomena in micro-electro mechanical systems devices with fluid mechanical applications. This paper aims to investigate the quenching behavior of numerical solutions for a two-dimensional semilinear wave equation with an inverse power law term. Design/methodology/approach: The localized radial basis function-generated finite difference (RBF-FD) method is used for approximating numerical solutions in space, and the finite difference scheme is used for temporal discretization. A discrete energy analysis is conducted to evaluate the local stability of the developed numerical scheme. Findings: The energy functional of the classical solution is defined. The numerical results demonstrate finite-time quenching, and the influence of various parameters is assessed through detailed numerical simulation. Originality/value: An RBF-FD approach is applied to confront the quenching phenomena in one- and two-dimensional cases. Stability and the computational performance of the proposed numerical scheme are verified numerically. The impact of various parameters and domains on quenching time is studied in detail. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of International Journal of Numerical Methods for Heat & Fluid Flow is the property of Emerald Publishing Limited 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: 32
        StartPage: 1825
    Subjects:
      – SubjectFull: Radial basis functions
        Type: general
      – SubjectFull: Nonlinear wave equations
        Type: general
      – SubjectFull: Finite difference method
        Type: general
      – SubjectFull: Stability theory
        Type: general
      – SubjectFull: Numerical analysis
        Type: general
      – SubjectFull: Microelectromechanical systems
        Type: general
      – SubjectFull: Energy function
        Type: general
    Titles:
      – TitleFull: A localized radial basis function-based approach for quenching phenomenon of two-dimensional semilinear wave equation.
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Singh, Shreya
      – PersonEntity:
          Name:
            NameFull: Burman, Riya Kumari
      – PersonEntity:
          Name:
            NameFull: Pandey, Rajesh K.
      – PersonEntity:
          Name:
            NameFull: Xu, Yufeng
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 05
              Text: 2026
              Type: published
              Y: 2026
          Identifiers:
            – Type: issn-print
              Value: 09615539
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              Value: 36
            – Type: issue
              Value: 5
          Titles:
            – TitleFull: International Journal of Numerical Methods for Heat & Fluid Flow
              Type: main
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