Semi-implicit ODE solver for matrix Riccati equation

@article{Butusov2016SemiimplicitOS,
  title={Semi-implicit ODE solver for matrix Riccati equation},
  author={D. N. Butusov and Timur I. Karimov and V. Y. Ostrovskii},
  journal={2016 IEEE NW Russia Young Researchers in Electrical and Electronic Engineering Conference (EIConRusNW)},
  year={2016},
  pages={168-172}
}
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.