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Stability and convergence of 3-point WSGD schemes for two-sided space fractional advection-diffusion equations with variable coefficients.

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Title: Stability and convergence of 3-point WSGD schemes for two-sided space fractional advection-diffusion equations with variable coefficients.
Authors: Lin, Fu-Rong1 (AUTHOR), She, Zi-Hang1,2 (AUTHOR) zhshe@hstc.edu.cn
Source: Applied Numerical Mathematics. Sep2021, Vol. 167, p281-307. 27p.
Subjects: Advection-diffusion equations
Abstract: In this paper, we consider high order numerical methods for the solution of the initial-boundary value problem of two-sided space fractional advection-diffusion equations (SFADEs). We use the Crank-Nicolson (CN) technique to discretize the temporal derivative, and apply 3-point weighted and shifted Grünwald difference (WSGD) operators to discretize the fractional derivatives of order α ∈ (1 , 2) and fractional derivatives of order β ∈ (0 , 1) , respectively. As a result, a new family of CN-WSGD schemes for SFADEs with temporally 2nd order and spatially j th order (j ≥ 2) accuracy are obtained. We then analyse the stability and the convergence of the numerical schemes. The extrapolated WSGD (EWSGD) operators are also discussed. Numerical examples are implemented to verify the theoretical results. [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.)
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  Data: Stability and convergence of 3-point WSGD schemes for two-sided space fractional advection-diffusion equations with variable coefficients.
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  Data: <searchLink fieldCode="AR" term="%22Lin%2C+Fu-Rong%22">Lin, Fu-Rong</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22She%2C+Zi-Hang%22">She, Zi-Hang</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> zhshe@hstc.edu.cn</i>
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  Data: In this paper, we consider high order numerical methods for the solution of the initial-boundary value problem of two-sided space fractional advection-diffusion equations (SFADEs). We use the Crank-Nicolson (CN) technique to discretize the temporal derivative, and apply 3-point weighted and shifted Grünwald difference (WSGD) operators to discretize the fractional derivatives of order α ∈ (1 , 2) and fractional derivatives of order β ∈ (0 , 1) , respectively. As a result, a new family of CN-WSGD schemes for SFADEs with temporally 2nd order and spatially j th order (j ≥ 2) accuracy are obtained. We then analyse the stability and the convergence of the numerical schemes. The extrapolated WSGD (EWSGD) operators are also discussed. Numerical examples are implemented to verify the theoretical results. [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:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1016/j.apnum.2021.05.007
    Languages:
      – Code: eng
        Text: English
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      Pagination:
        PageCount: 27
        StartPage: 281
    Subjects:
      – SubjectFull: Advection-diffusion equations
        Type: general
    Titles:
      – TitleFull: Stability and convergence of 3-point WSGD schemes for two-sided space fractional advection-diffusion equations with variable coefficients.
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            NameFull: Lin, Fu-Rong
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            NameFull: She, Zi-Hang
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            – D: 01
              M: 09
              Text: Sep2021
              Type: published
              Y: 2021
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              Value: 167
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            – TitleFull: Applied Numerical Mathematics
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