Exact solution of a simple time-dependent integro-differential equation by the method of Laplace transform and the theory of linear singular operators

The simplest form of the equation of transfer for a time dependent radiation field in finite atmosphere is considered. This equation of transfer is an integro-differential equation, the solution of this equation is based on the theory of separation of variables, the Laplace transform and the theory of linear singular operators. The emergent intensities from the bounding faces of the finite atmosphere are determined in terms of X-Y equations of Chandrasekhar. (orig.)