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A localized Fourier collocation method for the numerical solution of nonlinear fractional Fisher–Kolmogorov equation.

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Title: A localized Fourier collocation method for the numerical solution of nonlinear fractional Fisher–Kolmogorov equation.
Authors: Safari, Farzaneh1 (AUTHOR), Lin, Ji1,2 (AUTHOR) linji@hhu.edu.cn, Duan, Yanjun1 (AUTHOR)
Source: Computers & Mathematics with Applications. Sep2025, Vol. 193, p241-252. 12p.
Subjects: Collocation methods, Separation of variables, Linear equations, Fourier series, Sparse matrices, Quasilinearization
Abstract: This paper deals with a meshless method based on the localized Fourier collocation method (LFCM) combined with time discretization schemes to rigorously compute solutions for the Fisher-Kolmogorov equation. The idea is to generate the solution as the expansion of the modified Fourier series on the local subdomain and to use the reconstruction parameter to impact the accuracy and the rate of convergence. As applications, solutions of the factional Fisher-Kolmogorov equation on linear and nonlinear irregular domain are rigorously computed. Moreover, additional fourth-order terms in this model the so-called factional extended Fisher-Kolmogorov equation can be treated as a linear problem using the quasilinearization technique. Finally, we present an error analysis based on the illustration of convergence and accuracy graphs. [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
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DbLabel: Engineering Source
An: 186591019
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  Data: A localized Fourier collocation method for the numerical solution of nonlinear fractional Fisher–Kolmogorov equation.
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  Data: <searchLink fieldCode="AR" term="%22Safari%2C+Farzaneh%22">Safari, Farzaneh</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Lin%2C+Ji%22">Lin, Ji</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> linji@hhu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Duan%2C+Yanjun%22">Duan, Yanjun</searchLink><relatesTo>1</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Computers+%26+Mathematics+with+Applications%22">Computers & Mathematics with Applications</searchLink>. Sep2025, Vol. 193, p241-252. 12p.
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  Data: <searchLink fieldCode="DE" term="%22Collocation+methods%22">Collocation methods</searchLink><br /><searchLink fieldCode="DE" term="%22Separation+of+variables%22">Separation of variables</searchLink><br /><searchLink fieldCode="DE" term="%22Linear+equations%22">Linear equations</searchLink><br /><searchLink fieldCode="DE" term="%22Fourier+series%22">Fourier series</searchLink><br /><searchLink fieldCode="DE" term="%22Sparse+matrices%22">Sparse matrices</searchLink><br /><searchLink fieldCode="DE" term="%22Quasilinearization%22">Quasilinearization</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: This paper deals with a meshless method based on the localized Fourier collocation method (LFCM) combined with time discretization schemes to rigorously compute solutions for the Fisher-Kolmogorov equation. The idea is to generate the solution as the expansion of the modified Fourier series on the local subdomain and to use the reconstruction parameter to impact the accuracy and the rate of convergence. As applications, solutions of the factional Fisher-Kolmogorov equation on linear and nonlinear irregular domain are rigorously computed. Moreover, additional fourth-order terms in this model the so-called factional extended Fisher-Kolmogorov equation can be treated as a linear problem using the quasilinearization technique. Finally, we present an error analysis based on the illustration of convergence and accuracy graphs. [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:
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      – Type: doi
        Value: 10.1016/j.camwa.2025.06.020
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 12
        StartPage: 241
    Subjects:
      – SubjectFull: Collocation methods
        Type: general
      – SubjectFull: Separation of variables
        Type: general
      – SubjectFull: Linear equations
        Type: general
      – SubjectFull: Fourier series
        Type: general
      – SubjectFull: Sparse matrices
        Type: general
      – SubjectFull: Quasilinearization
        Type: general
    Titles:
      – TitleFull: A localized Fourier collocation method for the numerical solution of nonlinear fractional Fisher–Kolmogorov equation.
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            NameFull: Safari, Farzaneh
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            NameFull: Lin, Ji
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            NameFull: Duan, Yanjun
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            – D: 01
              M: 09
              Text: Sep2025
              Type: published
              Y: 2025
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              Value: 193
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            – TitleFull: Computers & Mathematics with Applications
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