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Renormalized Coordinate Stretching: A Generalization of Shoot and Fit with Application to Stellar Structure

The standard shooting and fitting algorithm for non-linear two-point boundary value problems derives from conventional coordinate perturbation theory. We generalize the algorithm using the renormalized perturbation theory of strained coordinates. This allows for the introduction of an arbitrary function, which may be chosen to improve numerical convergence. An application to a problem in stellar structure exemplifies the algorithm and shows that, when used in conjunction with the standard procedure, it has superior convergence compared to the standard one alone.

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Work Title Renormalized Coordinate Stretching: A Generalization of Shoot and Fit with Application to Stellar Structure
Access
Open Access
Creators
  1. Peter D. Usher
Keyword
  1. Numerical analysis
  2. Renormalized Coordinate Stretching
  3. Singular Non-Linear Boundary Value Problems
  4. Poincaré-Lighthill Perturbation Theory
  5. Stellar Structure
License CC BY-NC-SA 4.0 (Attribution-NonCommercial-ShareAlike)
Work Type Article
Publisher
  1. International Journal of Astronomy and Astrophysics
Publication Date September 2013
Subject
  1. Computer Science
Language
  1. English
Publisher Identifier (DOI)
  1. http://dx.doi.org/10.4236/ijaa.2013.33039
Related URLs
  1. https://www.scirp.org/journal/paperinformation?paperid=36526
Deposited March 22, 2025

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Version 1
published

  • Created

    March 22, 2025 11:18 by pxu1

  • Updated

    March 22, 2025 11:18 by [unknown user]

  • Updated Keyword, Publisher Identifier (DOI), Subtitle, and 2 more Show Changes

    March 22, 2025 11:27 by pxu1

    Keyword
    • Numerical analysis, Renormalized Coordinate Stretching
    Publisher Identifier (DOI)
    • http://www.airitilibrary.com/Publication/alDetailedMesh?DocID=21614717-201309-201802050021-201802050021-353-361
    Subtitle
    • International Journal of Astronomy and Astrophysics
    Description
    • The standard shooting and fitting algorithm for non-linear two-point boundary value problems derives from conventional coordinate perturbation theory. We generalize the algorithm using the renormalized perturbation theory of strained coordinates. This allows for the introduction of an arbitrary function, which may be chosen to improve numerical convergence. An application to a problem in stellar structure exemplifies the algorithm and shows that, when used in conjunction with the standard procedure, it has superior convergence compared to the standard one alone.
    Publication Date
    • 2013
  • Added Creator Peter D. Usher

    March 22, 2025 11:28 by pxu1

  • Added Creator Peter D. Usher

    March 22, 2025 11:31 by pxu1

  • Updated

    March 22, 2025 11:36 by pxu1

  • Updated Creator Peter D. Usher

    March 22, 2025 11:37 by pxu1

  • Added Renormalized Coordinate Stretching_ A Generalization of Shoot and Fit with Application to Stellar Structure.htm

    March 22, 2025 11:40 by pxu1

  • Updated Subject, Language, Related URLs, and 1 more Show Changes

    March 22, 2025 11:42 by pxu1

    Subject
    • Computer Science
    Language
    • English
    Related URLs
    • https://www.scirp.org/journal/paperinformation?paperid=36526
    License
    • https://creativecommons.org/licenses/by-nc-sa/4.0/
  • Published

    March 22, 2025 11:42 by pxu1

Version 2
published

  • Created

    March 22, 2025 11:48 by pxu1

  • Deleted Creator Peter D. Usher

    March 22, 2025 11:52 by pxu1

  • Published

    March 22, 2025 11:53 by pxu1

  • Updated

    March 22, 2025 22:04 by [unknown user]

  • Updated Keyword, Subtitle, Publisher, and 2 more Show Changes

    May 28, 2025 15:50 by avs5190

    Keyword
    • Numerical analysis, Renormalized Coordinate Stretching
    • Numerical analysis, Renormalized Coordinate Stretching, Singular Non-Linear Boundary Value Problems, Poincaré-Lighthill Perturbation Theory, Stellar Structure
    Subtitle
    • International Journal of Astronomy and Astrophysics
    Publisher
    • International Journal of Astronomy and Astrophysics
    Publisher Identifier (DOI)
    • http://www.airitilibrary.com/Publication/alDetailedMesh?DocID=21614717-201309-201802050021-201802050021-353-361
    • http://dx.doi.org/10.4236/ijaa.2013.33039
    Publication Date
    • 2013
    • 2013-09

Version 3
published

  • Created

    May 29, 2025 10:42 by pxu1

  • Deleted Renormalized Coordinate Stretching_ A Generalization of Shoot and Fit with Application to Stellar Structure.htm

    May 29, 2025 10:46 by pxu1

  • Added ijaa_shoot and fit.pdf

    May 29, 2025 11:22 by pxu1

  • Published

    May 29, 2025 11:23 by pxu1

Version 4
published

  • Created

    May 29, 2025 11:45 by pxu1

  • Updated

    May 29, 2025 11:46 by pxu1

  • Deleted ijaa_shoot and fit.pdf

    May 29, 2025 11:47 by pxu1

  • Added ad413046-7d36-4317-ac6b-1396b689236f.tmp

    May 29, 2025 11:49 by pxu1

  • Published

    May 29, 2025 11:49 by pxu1

Version 5
published

  • Created

    May 29, 2025 11:49 by pxu1

  • Deleted ad413046-7d36-4317-ac6b-1396b689236f.tmp

    May 29, 2025 11:53 by pxu1

  • Added ijaa_shoot and fit.pdf

    May 29, 2025 11:54 by pxu1

  • Published

    May 29, 2025 11:55 by pxu1

  • Updated

    May 29, 2025 22:05 by [unknown user]

Version 6
published

  • Created

    October 08, 2025 13:02 by avs5190

  • Deleted ijaa_shoot and fit.pdf

    October 08, 2025 13:02 by avs5190

  • Added AccessibleCopy_6-26_Renormalized_Coordinate_Stretching-tagged.pdf

    October 08, 2025 13:02 by avs5190

  • Published

    October 08, 2025 13:02 by avs5190