The Generalized Riccati Transformation as a Simple Alternative to Invariant Imbedding

A general linear two-point boundary-value problem of the type encountered in transfer theory is reduced to a set of initial-value problems by a transformation to uncoupled variables. The matrix of this transformation is shown to be the usual reflection matrix of invariant imbedding while the transformed variables describe the effect of non-homogeneous terms in the equations This method yields the interior solution as well as the solution at the boundary. It is shown that the method provides a suitable numerical procedure for subcritical problems. By a slight adaptation the method is shown to work for the most general type of linear boundary conditions. The relationship of this method to invariant imbedding and the relative advantages of each are discussed.