Graduate Numerically solving matrix Riccati ODE

[Avatrin]

Hi

I need to solve an equation of the form $$\dot{X}(t) = FX(t) + X(t)F^T + B$$
All of these are matrices. I have an initial condition X(0)=X_0.

However, I have no idea how to proceed. How can I make any progress?

 

[scottdave]

The Wikipedia page gives a general overview. https://en.wikipedia.org/wiki/Algebraic_Riccati_equation

But at the bottom there are some links to some MATLAB and Python resources which may help.

 

[Avatrin]

The Wikipedia page gives a general overview. https://en.wikipedia.org/wiki/Algebraic_Riccati_equation

But at the bottom there are some links to some MATLAB and Python resources which may help.

Well, I've already skimmed through that one. It is about the algebraic Riccati equation, and does mention that it can be applied to the differential Riccati equation. However, I just don't know how.

So, my best idea at the moment is just to use Euler's method. However, I wish I could find out how CARE can be used to solve my problem.

 

[bigfooted]

if you have matlab, just try the runge-kutta solver for solving ode's and systems of ode's. You can also use Euler's methods, as it is the simplest numerical method, but it is not always very stable.