  We consider differential Lyapunov and Riccati equations, and generalized
versions thereof. Such equations arise in many different areas and are
especially important within the field of optimal control. In order to
approximate their solution, one may use several different kinds of numerical
methods. Of these, splitting schemes are often a very competitive choice. In
this article, we investigate the use of graphical processing units (GPUs) to
parallelize such schemes and thereby further increase their effectiveness.
According to our numerical experiments, large speed-ups are often observed for
sufficiently large matrices. We also provide a comparison between different
splitting strategies, demonstrating that splitting the equations into a
moderate number of subproblems is generally optimal.
