Variational solution to the radiative equation by the use of a step function. II - Extension to nonlinear case by iteration method.

Abstract

The use of a stepwise constant trial function for the variational method has been extended to solve the nonlinear integral equation, frequently involved with the radiative transfer and the boundary value problems in Kinetic theory: The nonlinear integral equation is represented by a series of linear integral equations with the aid of a modified successive approximation method and solved by the variational technique applied for the linear integral equation. The solutions, in terms of temperature and radiative flux, are presented numerically and are compared with the exact solution. Numerical solutions presented in this report are limited to the absorption coefficient of the Milne-Eddington type, pKv = av j$(p, T). The method is simple, straightforward and provides excellent accuracy in the solution with a minor computing time.