Invariant imbedding and order-of-scattering theory in radiation field

AbstractAround fifty years ago, the principles of invariance were introduced in the the study of radiative transfer in planetary atmospheres and then extensively extended to astrophysics by Ambarzumian and Chandrasekhar. Furthermore, the invariance concept was pursued and generalized by Bellman, Kalaba and Wing, who gave the term “Invariant Imbedding” for the systematic use of invariance concept and functionals in various problems of mathematical physics and engineering. Then the two-points boundary value problem was transformed into the initial value problem.In the present paper, starting from the low-order of scattering and transmission functions, the higher order of these global functions is approximated with the aid of invariant imbedding expression and then the initial value solution of the two components radiation field has been also dealt with