Semi-implicit ODE solver for matrix Riccati equation

In this paper we consider the numerical solution of matrix Riccati equation with the different ODE solvers. A comparison of following extrapolation methods is undertaken: Gragg-Bulirsch-Stoer's (GBS) explicit midpoint rule, implicit midpoint rule, and new semi-implicit D-methods. The study showed that D-methods, being a trade-off between explicit and implicit methods, can be an effective solution for computer simulation of matrix Riccati equation.