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Renormalized Coordinate Stretching: A Generalization of Shoot and Fit with Application to Stellar Structure
Department of Astronomy and Astrophysics, The Pennsylvania State University, University Park, USA
- 1 Department of Astronomy and Astrophysics, The Pennsylvania State University, University Park, USA
International Journal of Astronomy and Astrophysics·Volume 03 (2013)·Pages 353–361·Published 23 August 2013·DOI10.4236/ijaa.2013.33039
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Abstract
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.
KeywordsSingular Non-Linear Boundary Value ProblemsRenormalized Coordinate StretchingPoincaré-Lighthill Perturbation TheoryNumerical AnalysisStellar Structure
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