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 IJAA  Vol.3 No.3 , September 2013
Renormalized Coordinate Stretching: A Generalization of Shoot and Fit with Application to Stellar Structure
Peter D. Usher
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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.
Keywords: Singular Non-Linear Boundary Value Problems; Renormalized Coordinate Stretching; Poincaré-Lighthill Perturbation Theory; Numerical Analysis; Stellar Structure
Cite this paper: P. Usher, "Renormalized Coordinate Stretching: A Generalization of Shoot and Fit with Application to Stellar Structure," International Journal of Astronomy and Astrophysics, Vol. 3 No. 3, 2013, pp. 353-361. doi: 10.4236/ijaa.2013.33039.
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