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Advanced higher order Haar wavelet - Quasilinearization approach for nonlinear singular BVPs.

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Title: Advanced higher order Haar wavelet - Quasilinearization approach for nonlinear singular BVPs.
Authors: Yadav, Ankita1 (AUTHOR), Kumar, Narendra2 (AUTHOR), Verma, Amit K.1 (AUTHOR) akverma@iitp.ac.in
Source: Applied Numerical Mathematics. Sep2026, Vol. 227, p151-168. 18p.
Subjects: Quasilinearization, Nonlinear boundary value problems, Wavelets (Mathematics), Collocation methods, Numerical analysis, Integrals
Abstract: We propose a numerical method called the higher-order Haar wavelet collocation method, combined with quasilinearization techniques. The proposed method can effectively solve a wide range of nonlinear singular second-order boundary value problems under certain sufficient conditions. The key objective of adopting this advanced version of the Haar wavelet collocation method is to achieve high accuracy and rapid convergence while minimizing the absolute error. Several test examples are presented, and their numerical solutions are compared with the proposed numerical method and existing state-of-the-art techniques. The results show that the proposed technique reduces the computational cost and provides more accurate solutions than the bvp4c MATLAB solver. [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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Header DbId: egs
DbLabel: Engineering Source
An: 194123930
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  Data: Advanced higher order Haar wavelet - Quasilinearization approach for nonlinear singular BVPs.
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  Data: <searchLink fieldCode="AR" term="%22Yadav%2C+Ankita%22">Yadav, Ankita</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Kumar%2C+Narendra%22">Kumar, Narendra</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Verma%2C+Amit+K%2E%22">Verma, Amit K.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> akverma@iitp.ac.in</i>
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  Data: <searchLink fieldCode="JN" term="%22Applied+Numerical+Mathematics%22">Applied Numerical Mathematics</searchLink>. Sep2026, Vol. 227, p151-168. 18p.
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  Data: <searchLink fieldCode="DE" term="%22Quasilinearization%22">Quasilinearization</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+boundary+value+problems%22">Nonlinear boundary value problems</searchLink><br /><searchLink fieldCode="DE" term="%22Wavelets+%28Mathematics%29%22">Wavelets (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Collocation+methods%22">Collocation methods</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Integrals%22">Integrals</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: We propose a numerical method called the higher-order Haar wavelet collocation method, combined with quasilinearization techniques. The proposed method can effectively solve a wide range of nonlinear singular second-order boundary value problems under certain sufficient conditions. The key objective of adopting this advanced version of the Haar wavelet collocation method is to achieve high accuracy and rapid convergence while minimizing the absolute error. Several test examples are presented, and their numerical solutions are compared with the proposed numerical method and existing state-of-the-art techniques. The results show that the proposed technique reduces the computational cost and provides more accurate solutions than the bvp4c MATLAB solver. [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.2026.05.003
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 18
        StartPage: 151
    Subjects:
      – SubjectFull: Quasilinearization
        Type: general
      – SubjectFull: Nonlinear boundary value problems
        Type: general
      – SubjectFull: Wavelets (Mathematics)
        Type: general
      – SubjectFull: Collocation methods
        Type: general
      – SubjectFull: Numerical analysis
        Type: general
      – SubjectFull: Integrals
        Type: general
    Titles:
      – TitleFull: Advanced higher order Haar wavelet - Quasilinearization approach for nonlinear singular BVPs.
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            NameFull: Yadav, Ankita
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            NameFull: Kumar, Narendra
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            NameFull: Verma, Amit K.
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          Dates:
            – D: 01
              M: 09
              Text: Sep2026
              Type: published
              Y: 2026
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              Value: 01689274
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              Value: 227
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            – TitleFull: Applied Numerical Mathematics
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