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Generalized Clenshaw-Curtis quadrature method for systems of linear ODEs with constant coefficients.

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Title: Generalized Clenshaw-Curtis quadrature method for systems of linear ODEs with constant coefficients.
Authors: Lin, Fu-Rong1 (AUTHOR) frlin@stu.edu.cn, Yang, Xi1 (AUTHOR), Zhang, Gui-Rong1 (AUTHOR)
Source: Applied Numerical Mathematics. Nov2025, Vol. 217, p112-125. 14p.
Subjects: Linear differential equations, Numerical analysis, Matrix exponential, Numerical integration, Heat conduction, Initial value problems
Abstract: In this paper, we consider high precision numerical methods for the initial problem of systems of linear ordinary differential equations (ODEs) with constant coefficients. It is well-known that the analytic solution of such a system of linear ODEs involves a matrix exponential function and an integral whose integrand is the product of a matrix exponential and a vector-valued function. We mainly consider numerical quadrature methods for the integral term in the analytic solution and propose a generalized Clenshaw-Curtis (GCC) quadrature method. The proposed method is then applied to the initial-boundary value problem for a heat conduction equation and a Riesz space fractional diffusion equation, respectively. Numerical results are presented to demonstrate the effectiveness of the proposed method. [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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An: 187263824
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  Data: Generalized Clenshaw-Curtis quadrature method for systems of linear ODEs with constant coefficients.
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  Data: <searchLink fieldCode="AR" term="%22Lin%2C+Fu-Rong%22">Lin, Fu-Rong</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> frlin@stu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Yang%2C+Xi%22">Yang, Xi</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Zhang%2C+Gui-Rong%22">Zhang, Gui-Rong</searchLink><relatesTo>1</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Applied+Numerical+Mathematics%22">Applied Numerical Mathematics</searchLink>. Nov2025, Vol. 217, p112-125. 14p.
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  Data: <searchLink fieldCode="DE" term="%22Linear+differential+equations%22">Linear differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Matrix+exponential%22">Matrix exponential</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+integration%22">Numerical integration</searchLink><br /><searchLink fieldCode="DE" term="%22Heat+conduction%22">Heat conduction</searchLink><br /><searchLink fieldCode="DE" term="%22Initial+value+problems%22">Initial value problems</searchLink>
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  Label: Abstract
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  Data: In this paper, we consider high precision numerical methods for the initial problem of systems of linear ordinary differential equations (ODEs) with constant coefficients. It is well-known that the analytic solution of such a system of linear ODEs involves a matrix exponential function and an integral whose integrand is the product of a matrix exponential and a vector-valued function. We mainly consider numerical quadrature methods for the integral term in the analytic solution and propose a generalized Clenshaw-Curtis (GCC) quadrature method. The proposed method is then applied to the initial-boundary value problem for a heat conduction equation and a Riesz space fractional diffusion equation, respectively. Numerical results are presented to demonstrate the effectiveness of the proposed method. [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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      – Type: doi
        Value: 10.1016/j.apnum.2025.06.003
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      – Code: eng
        Text: English
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        PageCount: 14
        StartPage: 112
    Subjects:
      – SubjectFull: Linear differential equations
        Type: general
      – SubjectFull: Numerical analysis
        Type: general
      – SubjectFull: Matrix exponential
        Type: general
      – SubjectFull: Numerical integration
        Type: general
      – SubjectFull: Heat conduction
        Type: general
      – SubjectFull: Initial value problems
        Type: general
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      – TitleFull: Generalized Clenshaw-Curtis quadrature method for systems of linear ODEs with constant coefficients.
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            – D: 01
              M: 11
              Text: Nov2025
              Type: published
              Y: 2025
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