OverflowError: (34, 'Result too large') on the resolution of a differential equation with Euler method

Question

I'm trying to solve a differential equation for a physical problem : the falling of a golf ball. I am using the Euler resolution method, and I have this code :

def F(Z, t):
    res = [Z[1], (-K/m)*Z[1]*sqrt((Z[1]**2) + (Z[1]**2)), Z[3], (-K/m)*Z[3]*sqrt((Z[3]**2) + (Z[3]**2))]
    return res

def reso_z_euler(liste_t, F, CI, K):
    n = len(liste_t)
    Z = CI
    pas = (liste_t[-1] - liste_t[0])/(n-1)
    listeZ = [Z]
    for i in range(1, n):
        Z = F(Z, temps[i-1])
        listeZ.append(Z)
    return listeZ

listeZ = reso_z_euler(temps, F, Z0, K)

When I run this code, the terminal throws an error : OverflowError: (34, 'Result too large') I have never seen this error and I don't know what to do.. Your help would be so nice.. Thanks

Answer 1

• You are using an unknown or non-local array for the times, temps instead of liste_t

• You are not implementing the Euler method Z = Z + pas*F(Z,liste_t[i-1]) , you would have to employ some mechanism to implement the vector arithmetic, for instance

  Z = [ zk+pas*fk for zk, fk in zip(Z, F(Z,liste_t[i-1])) ]

• You forgot to include the gravity force in the derivatives computation.

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In general, the Euler method is only good to learn the principles of numerical ODE integration, for any useful result use a higher order method.