Solution of a nonsymmetric algebraic Riccati equation from a two-dimensional transport model

For the steady-state solution of an integral–differential equation from a two-dimensional model in transport theory, we shall derive and study a nonsymmetric algebraic Riccati equation B--XF--F+X+XB+X=0, where , and with a nonnegative matrix P, positive diagonal matrices D±, and nonnegative parameters f, and . We prove the existence of the minimal nonnegative solution X∗ under the physically reasonable assumption , and study its numerical computation by fixed-point iteration, Newton’s method and doubling. We shall also study several special cases; e.g. when and P is low-ranked, then is low-ranked and can be computed using more efficient iterative processes in U and V. Numerical examples will be given to illustrate our theoretical results.