Existence of algebraic matrix Riccati equations arising in transport theory Original Research Article

We consider the existence of positive solutions of a certain class of algebraic matrix Riccati equations with two parameters, c (0 less-than-or-equals, slant c less-than-or-equals, slant 1) and α (0 less-than-or-equals, slant α less-than-or-equals, slant 1). Here c denotes the fraction of scattering per collision, and α 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.