Astronomy and Astrophysics – Astrophysics
Scientific paper
Aug 1978
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978ap%26ss..57..469s&link_type=abstract
Astrophysics and Space Science, vol. 57, no. 2, Aug. 1978, p. 469-478.
Astronomy and Astrophysics
Astrophysics
Atmospheric Scattering, Integral Equations, Milne Method, Variational Principles, Algorithms, Isotropic Media, Light Scattering
Scientific paper
A general variational method based on a flexible computational algorithm is developed for the solution of Milne's integral equation. Huang's (1953) resolvent function is employed, so that the variational system of equations for the unknown parameters is linear, and a general trial approximate solution is chosen which conforms to Hopf's condition. The basic equations governing the variational method are expressed in explicit general forms, recurrence relations are obtained for various elements and functions, and a recursive computational algorithm is constructed. The approximate solution for the case N = 20 is presented to illustrate the precision of the proposed method. A comparison of the numerical results with those calculated by King et al. (1965) using the method of discrete ordinates based on the double-Gauss quadrature formula with 64 ordinates shows extremely good agreement to six-digit accuracy.
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