AN ITERATIVE SOLUTION OF AN INTEGRAL EQUATION FOR RADIATIVE TRANSFER BY USING VARIATIONAL TECHNIQUE

摘要

An effective iterative technique is introduced to solve a nonlinear integral equation frequently associated with radiative transfer problems. The problem is formulated in such a way that each step of an iterative sequence requires the so solution of a linear integral equation. The advantage of a previously introduced variational technique which utilizes a stepwise constant trial function is exploited in this report to cope with the nonlinear problem. The method is simple and straightforward. Rapid convergence is obtained by employing a linear inter¬polation of the iterative solutions. Using absorption coefficients of the Milne-Eddington type, ρKν = ανβ(ρ,T) which are applicable to some planetary atmospheric radiation problems, solutions are found in terms of temperature and radiative flux. These solutions are presented numerically and show excellent agreement with other numerical solutions.