Article citationsMore>>

M. J. Lighthill, “A Technique for Rendering Approximate Solutions to Physical Problems Uniformly Convergent,” Philosophical Magazine, Vol. 40, 1949, pp. 1179-1201.

has been cited by the following article:

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

  AUTHORS: Peter D. Usher

  KEYWORDS: Singular Non-Linear Boundary Value Problems; Renormalized Coordinate Stretching; Poincaré-Lighthill Perturbation Theory; Numerical Analysis; Stellar Structure

  JOURNAL NAME: International Journal of Astronomy and Astrophysics, Vol.3 No.3, September 3, 2013

  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.