EXISTENCE OF ALGEBRAIC MATRIX RICCATI-EQUATIONS ARISING IN TRANSPORT-THEORY

Abstract

We consider the existence of positive solutions of a certain class of algebraic matrix Riccati equations with two parameters, c (0 less than or equal to c less than or equal to 1) and alpha (0 less than or equal to alpha less than or equal to 1). Here c denotes the fraction of scattering per collision, and cu is an angular shift. Equations of this class are induced via invariant imbedding and the shifted Gauss-Legendre quadrature formula from a simple transport model. By establishing the existence of positive solutions of such equations, the problem of the convergence of some iterative schemes for solving them can be completely solved.