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Employing CNPS and CPS approaches to calculate numerical roots of ninth-order linear and nonlinear boundary value problems.

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Title: Employing CNPS and CPS approaches to calculate numerical roots of ninth-order linear and nonlinear boundary value problems.
Authors: Khalid, Aasma1 (AUTHOR) aasmakhalid@gcwuf.edu.pk, Haq, Inamul1 (AUTHOR) inamulhaq@gcwuf.edu.pk, Rehan, Akmal2 (AUTHOR) akmalrehan@uaf.edu.pk, Alshehri, Hashim M.3 (AUTHOR) hmalshehri@kau.edu.sa, Osman, M. S.4 (AUTHOR) mofatzi@cu.edu.eg
Source: International Journal of Modern Physics C: Computational Physics & Physical Computation. Oct2024, Vol. 35 Issue 10, p1-28. 28p.
Subjects: Nonlinear boundary value problems, Numerical roots, Boundary value problems, Splines, Finite differences
Abstract: The extremely accurate findings of ninth-order linear and nonlinear BVPs are described in this paper. CNPS and CPS are used to find out the numerical roots of linear and nonlinear, ninth-order BVPs. The proposed methods transform the ninth-order BVPs into a system of linear equations. The algorithms developed in this study not only provide approximate solutions to the BVPs using CNPS and CPS, but they also estimate the derivatives from the first to the ninth-order of the analytical solution simultaneously. These approaches are implemented across five diverse problems, showcasing the effectiveness of these techniques by utilizing step sizes of h = 1 / 1 0 and h = 1 / 5. In order to gauge the accuracy of the methods, a comparison is drawn between the outcomes and the exact solutions, which are then presented in tabular and graphical format. The precision of these techniques is demonstrated through a detailed investigation and is found to be superior to the CBS, the Petrov–Galerkin Method (PGM) using Splines functions as basis functions and Septic B Splines functions as weight functions, the collocation method for ninth-order BVPs by Quintic B Splines and Sextic B Splines as evidenced by the comparison of AEs of CPS and CNPS with these alternative methods. [ABSTRACT FROM AUTHOR]
Copyright of International Journal of Modern Physics C: Computational Physics & Physical Computation 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: 180476281
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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  Label: Title
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  Data: Employing CNPS and CPS approaches to calculate numerical roots of ninth-order linear and nonlinear boundary value problems.
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  Data: <searchLink fieldCode="AR" term="%22Khalid%2C+Aasma%22">Khalid, Aasma</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> aasmakhalid@gcwuf.edu.pk</i><br /><searchLink fieldCode="AR" term="%22Haq%2C+Inamul%22">Haq, Inamul</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> inamulhaq@gcwuf.edu.pk</i><br /><searchLink fieldCode="AR" term="%22Rehan%2C+Akmal%22">Rehan, Akmal</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> akmalrehan@uaf.edu.pk</i><br /><searchLink fieldCode="AR" term="%22Alshehri%2C+Hashim+M%2E%22">Alshehri, Hashim M.</searchLink><relatesTo>3</relatesTo> (AUTHOR)<i> hmalshehri@kau.edu.sa</i><br /><searchLink fieldCode="AR" term="%22Osman%2C+M%2E+S%2E%22">Osman, M. S.</searchLink><relatesTo>4</relatesTo> (AUTHOR)<i> mofatzi@cu.edu.eg</i>
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  Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Modern+Physics+C%3A+Computational+Physics+%26+Physical+Computation%22">International Journal of Modern Physics C: Computational Physics & Physical Computation</searchLink>. Oct2024, Vol. 35 Issue 10, p1-28. 28p.
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  Data: <searchLink fieldCode="DE" term="%22Nonlinear+boundary+value+problems%22">Nonlinear boundary value problems</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+roots%22">Numerical roots</searchLink><br /><searchLink fieldCode="DE" term="%22Boundary+value+problems%22">Boundary value problems</searchLink><br /><searchLink fieldCode="DE" term="%22Splines%22">Splines</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+differences%22">Finite differences</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: The extremely accurate findings of ninth-order linear and nonlinear BVPs are described in this paper. CNPS and CPS are used to find out the numerical roots of linear and nonlinear, ninth-order BVPs. The proposed methods transform the ninth-order BVPs into a system of linear equations. The algorithms developed in this study not only provide approximate solutions to the BVPs using CNPS and CPS, but they also estimate the derivatives from the first to the ninth-order of the analytical solution simultaneously. These approaches are implemented across five diverse problems, showcasing the effectiveness of these techniques by utilizing step sizes of h = 1 / 1 0 and h = 1 / 5. In order to gauge the accuracy of the methods, a comparison is drawn between the outcomes and the exact solutions, which are then presented in tabular and graphical format. The precision of these techniques is demonstrated through a detailed investigation and is found to be superior to the CBS, the Petrov–Galerkin Method (PGM) using Splines functions as basis functions and Septic B Splines functions as weight functions, the collocation method for ninth-order BVPs by Quintic B Splines and Sextic B Splines as evidenced by the comparison of AEs of CPS and CNPS with these alternative methods. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of International Journal of Modern Physics C: Computational Physics & Physical Computation 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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      – Type: doi
        Value: 10.1142/S0129183124501213
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 28
        StartPage: 1
    Subjects:
      – SubjectFull: Nonlinear boundary value problems
        Type: general
      – SubjectFull: Numerical roots
        Type: general
      – SubjectFull: Boundary value problems
        Type: general
      – SubjectFull: Splines
        Type: general
      – SubjectFull: Finite differences
        Type: general
    Titles:
      – TitleFull: Employing CNPS and CPS approaches to calculate numerical roots of ninth-order linear and nonlinear boundary value problems.
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            NameFull: Khalid, Aasma
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            NameFull: Haq, Inamul
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            NameFull: Rehan, Akmal
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            NameFull: Alshehri, Hashim M.
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            NameFull: Osman, M. S.
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            – D: 01
              M: 10
              Text: Oct2024
              Type: published
              Y: 2024
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              Value: 35
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            – TitleFull: International Journal of Modern Physics C: Computational Physics & Physical Computation
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