Matrix ODE using Odeintw Python

Question

The odeintw example we get something like this:

def asys(a, t, c):
return c.dot(a)

c = np.array([[-0.5, -1.25],
              [ 0.5, -0.25]])
t = np.linspace(0, 10, 201)

# a0 is the initial condition.
a0 = np.array([[0.0, 2.0],
               [2.0, 3.0]])

# Call `odeintw`.
sol = odeintw(asys, a0, t, args=(c,))

But I wanna know if it is possible to solve a problem for a c that is time dependent. For it written like (example):

c = np.random.rand(201,2,2)

I would like to write a function that odeintw understand for each t one correspondent c. Can someone help me?

Lutz Lehmann Lutz Lehmann · Accepted Answer · 2020-07-27T21:49:23

The principal point to notice is that the ODE solver will evaluate the function asys at arbitrary values of t. Thus you will need to interpolate the function table for c. You would have to check if the existing interpolation functions can handle multi-dimensional arrays. Probably you will need a work-around or wrapper just like odeintw provides for odeint.

This will work very poorly, if at all, for the presented test example. A random array will give a very jumpy function table, while the ODE solver rely on the differential equation being smooth. Non-smooth behavior leads to very small step sizes and thus very many function evaluations.

Matrix ODE using Odeintw Python

1 Answers