Newton's Method for the Nonlinear Integral Equation for the H Function of Isotropic Scattering.

by H. H. Natsuyama, Robert E. Kalaba

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The application of a version of Newton's method to the numerical solution of a basic nonlinear integral equation in the theory of radiative transfer. A sequence of rapidly convergent approximations to the H function of Chandrasekhar is determined. The method evaluates integrals by means of a gaussian quadrature formula, and the resulting equations can be used to obtain values quickly and accurately. Using an IBM 7044 digital computer, computing time for the Newton method was approximately 5 to 10 seconds for all cases considered in the experiment. 12 pp. (KB)

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