ANALYTICAL AND NUMERICAL-SOLUTIONS OF SOME INTEGRAL-EQUATIONS IN RADIATION TRANSPORT-THEORY

We discuss some mathematical and computational problems relevant to th e solutions of both linear and non-linear integral equations arising i n radiation transport. By means of a functional-operator approach, ana lytic solutions for the FEL (Free Electron Laser) integral equations a re found in terms of Bessel-Clifford functions. As for applications of this method to non-linear equations, the same technique allows us to obtain an efficient yet simple algorithm for the numerical solution of the Ambartsumian-Chandrasekhar H-equation corresponding to a Neumann- series expansion.