GIP integrators for Matrix Riccati Differential Equations

This paper shows several classes of numerical algorithms, which we call GIP integrators, that can solve for X past its singularities. Furthermore, none of the algorithms require knowledge of the placement or even existence of singularities in X. Also, it is shown how embedded Runge-Kutta methods can be used to construct GIP integrators to not only approximate X past singularities but also provide for error estimation to allow efficient time stepping. Finally, several examples are shown to validate the theory.