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Numerical Method for Time Distributed-Order Diffusion Equations Based on Reproducing Kernel Space.

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Title: Numerical Method for Time Distributed-Order Diffusion Equations Based on Reproducing Kernel Space.
Authors: Zhang, Yingchao1 (AUTHOR) zhych0314@163.com, Jiang, Wei2 (AUTHOR), Li, Lin2 (AUTHOR), Lin, Yingzhen1 (AUTHOR)
Source: International Journal of Computational Methods. Feb2026, Vol. 23 Issue 1, p1-19. 19p.
Subjects: Reproducing kernel (Mathematics), Legendre's polynomials, Fractional powers, Heat equation, Numerical analysis, Simulation methods & models, Computer simulation
Abstract: A numerical method for time distributed-order diffusion equations based on reproducing kernel space is proposed. The distributed-order diffusion equations are transformed into a multinomial fractional-order diffusion equation by using the compound trapezoidal formula. To discuss approximate solutions to the fractional-order diffusion equation, we define a class of binary reproducing kernel space and construct an orthonormal basis of the space by Legendre polynomials. Based on the idea of least residue, the numerical method is given and the convergence analysis is carried out. The final numerical experiments verify the accuracy of our method. [ABSTRACT FROM AUTHOR]
Copyright of International Journal of Computational Methods is the property of World Scientific Publishing Company 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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Header DbId: egs
DbLabel: Engineering Source
An: 188151838
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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  Label: Title
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  Data: Numerical Method for Time Distributed-Order Diffusion Equations Based on Reproducing Kernel Space.
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  Data: <searchLink fieldCode="AR" term="%22Zhang%2C+Yingchao%22">Zhang, Yingchao</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> zhych0314@163.com</i><br /><searchLink fieldCode="AR" term="%22Jiang%2C+Wei%22">Jiang, Wei</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Li%2C+Lin%22">Li, Lin</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Lin%2C+Yingzhen%22">Lin, Yingzhen</searchLink><relatesTo>1</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Computational+Methods%22">International Journal of Computational Methods</searchLink>. Feb2026, Vol. 23 Issue 1, p1-19. 19p.
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  Data: <searchLink fieldCode="DE" term="%22Reproducing+kernel+%28Mathematics%29%22">Reproducing kernel (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Legendre's+polynomials%22">Legendre's polynomials</searchLink><br /><searchLink fieldCode="DE" term="%22Fractional+powers%22">Fractional powers</searchLink><br /><searchLink fieldCode="DE" term="%22Heat+equation%22">Heat equation</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Simulation+methods+%26+models%22">Simulation methods & models</searchLink><br /><searchLink fieldCode="DE" term="%22Computer+simulation%22">Computer simulation</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: A numerical method for time distributed-order diffusion equations based on reproducing kernel space is proposed. The distributed-order diffusion equations are transformed into a multinomial fractional-order diffusion equation by using the compound trapezoidal formula. To discuss approximate solutions to the fractional-order diffusion equation, we define a class of binary reproducing kernel space and construct an orthonormal basis of the space by Legendre polynomials. Based on the idea of least residue, the numerical method is given and the convergence analysis is carried out. The final numerical experiments verify the accuracy of our method. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of International Journal of Computational Methods is the property of World Scientific Publishing Company 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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    Identifiers:
      – Type: doi
        Value: 10.1142/S0219876225500380
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 19
        StartPage: 1
    Subjects:
      – SubjectFull: Reproducing kernel (Mathematics)
        Type: general
      – SubjectFull: Legendre's polynomials
        Type: general
      – SubjectFull: Fractional powers
        Type: general
      – SubjectFull: Heat equation
        Type: general
      – SubjectFull: Numerical analysis
        Type: general
      – SubjectFull: Simulation methods & models
        Type: general
      – SubjectFull: Computer simulation
        Type: general
    Titles:
      – TitleFull: Numerical Method for Time Distributed-Order Diffusion Equations Based on Reproducing Kernel Space.
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          Name:
            NameFull: Zhang, Yingchao
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            NameFull: Jiang, Wei
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            NameFull: Li, Lin
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            NameFull: Lin, Yingzhen
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            – D: 01
              M: 02
              Text: Feb2026
              Type: published
              Y: 2026
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              Value: 23
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            – TitleFull: International Journal of Computational Methods
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