How to solve Matrix Riccati ODE in python

Question

I want to solve the following Matrix Riccati ODE. My Matrix Riccati ODE After searching on the Internet, I found that there is something called continuous-time algebraic Riccati equation (CARE) https://docs.scipy.org/doc/scipy/reference/generated/scipy.linalg.solve_continuous_are.html#scipy.linalg.solve_continuous_are

However, I am not majored in math and not familiar with advanced ode, so I wanna ask that are these two the same thing or not? If not, how to solve the above Matrix Riccati ODE in Python? Thanks in advance. Any comments are welcomed.

Answer 1

You can use the modified Davison-Maki method to solve your Riccati equation. See https://arxiv.org/pdf/1910.13362.pdf (Algorithm 2). The method is easy to implement.