On a generalization of the matrix and scalar Riccati equation

Abstract

The usual Matrix Riccati equation can be related to the transport of a beam of particles through a medium of finite length with conservative type of interactions (R. Bellman, S. Ueno, and R. Vasudevan, On the matrix Riccati equation of transport processes, University of Southern California Technical Report No. 72-13). Varying the physical picture of the interactions in the medium, we arrive at extensions of the Riccati equations with higher order nonlinear terms. Using the physical picture to guide our intuition, we achieve a linearization of these generalized Riccati equations in this paper, and this procedure will assist numerical computation of the solution of such nonlinear equations in a substantial manner.