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Time-local discretization of fractional and related diffusive operators using Gaussian quadrature with applications.

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Title: Time-local discretization of fractional and related diffusive operators using Gaussian quadrature with applications.
Authors: Monteghetti, Florian1 (AUTHOR) florian.monteghetti@onera.fr, Matignon, Denis2 (AUTHOR) denis.matignon@isae.fr, Piot, Estelle1 (AUTHOR) estelle.piot@onera.fr
Source: Applied Numerical Mathematics. Sep2020, Vol. 155, p73-92. 20p.
Subjects: Fractional differential equations, Laplacian operator, Delay differential equations, Quadrature domains, Discretization methods, Eigenvalue equations, Fractional calculus
Abstract: This paper investigates the time-local discretization, using Gaussian quadrature, of a class of diffusive operators that includes fractional operators, for application in fractional differential equations and related eigenvalue problems. A discretization based on the Gauss–Legendre quadrature rule is analyzed both theoretically and numerically. Numerical comparisons with both optimization-based and quadrature-based methods highlight its applicability. In addition, it is shown, on the example of a fractional delay differential equation, that quadrature-based discretization methods are spectrally correct, i.e. that they yield an unpolluted and convergent approximation of the essential spectrum linked to the fractional derivative, by contrast with optimization-based methods that can yield polluted spectra whose convergence is difficult to assess. [ABSTRACT FROM AUTHOR]
Copyright of Applied Numerical Mathematics is the property of Elsevier B.V. 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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  Data: Time-local discretization of fractional and related diffusive operators using Gaussian quadrature with applications.
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  Data: <searchLink fieldCode="AR" term="%22Monteghetti%2C+Florian%22">Monteghetti, Florian</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> florian.monteghetti@onera.fr</i><br /><searchLink fieldCode="AR" term="%22Matignon%2C+Denis%22">Matignon, Denis</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> denis.matignon@isae.fr</i><br /><searchLink fieldCode="AR" term="%22Piot%2C+Estelle%22">Piot, Estelle</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> estelle.piot@onera.fr</i>
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  Data: <searchLink fieldCode="JN" term="%22Applied+Numerical+Mathematics%22">Applied Numerical Mathematics</searchLink>. Sep2020, Vol. 155, p73-92. 20p.
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  Data: <searchLink fieldCode="DE" term="%22Fractional+differential+equations%22">Fractional differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Laplacian+operator%22">Laplacian operator</searchLink><br /><searchLink fieldCode="DE" term="%22Delay+differential+equations%22">Delay differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Quadrature+domains%22">Quadrature domains</searchLink><br /><searchLink fieldCode="DE" term="%22Discretization+methods%22">Discretization methods</searchLink><br /><searchLink fieldCode="DE" term="%22Eigenvalue+equations%22">Eigenvalue equations</searchLink><br /><searchLink fieldCode="DE" term="%22Fractional+calculus%22">Fractional calculus</searchLink>
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  Label: Abstract
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  Data: This paper investigates the time-local discretization, using Gaussian quadrature, of a class of diffusive operators that includes fractional operators, for application in fractional differential equations and related eigenvalue problems. A discretization based on the Gauss–Legendre quadrature rule is analyzed both theoretically and numerically. Numerical comparisons with both optimization-based and quadrature-based methods highlight its applicability. In addition, it is shown, on the example of a fractional delay differential equation, that quadrature-based discretization methods are spectrally correct, i.e. that they yield an unpolluted and convergent approximation of the essential spectrum linked to the fractional derivative, by contrast with optimization-based methods that can yield polluted spectra whose convergence is difficult to assess. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Applied Numerical Mathematics is the property of Elsevier B.V. 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.apnum.2018.12.003
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 20
        StartPage: 73
    Subjects:
      – SubjectFull: Fractional differential equations
        Type: general
      – SubjectFull: Laplacian operator
        Type: general
      – SubjectFull: Delay differential equations
        Type: general
      – SubjectFull: Quadrature domains
        Type: general
      – SubjectFull: Discretization methods
        Type: general
      – SubjectFull: Eigenvalue equations
        Type: general
      – SubjectFull: Fractional calculus
        Type: general
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      – TitleFull: Time-local discretization of fractional and related diffusive operators using Gaussian quadrature with applications.
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            NameFull: Monteghetti, Florian
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            NameFull: Matignon, Denis
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            NameFull: Piot, Estelle
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          Dates:
            – D: 01
              M: 09
              Text: Sep2020
              Type: published
              Y: 2020
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              Value: 155
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