What am I doing wrong in this Dopri5 implementation

Question

I am totally new to python, and try to integrate following ode:

$\\dot{x} = -2x-y^2$

$\\dot{y} = -yx^2

This results in an array with everything 0 though What am I doing wrong? It is mostly copied code, and with another, not coupled ode it worked fine.

import numpy as np
import matplotlib.pyplot as plt
from scipy.integrate import ode


def fun(t, z):
    """
    Right hand side of the differential equations
      dx/dt = -omega * y
      dy/dt = omega * x
    """
    x, y = z
    f = [-2*x-y**2, -y-x**2]
    return f

# Create an `ode` instance to solve the system of differential
# equations defined by `fun`, and set the solver method to 'dop853'.
solver = ode(fun)
solver.set_integrator('dopri5')

# Set the initial value z(0) = z0.
t0 = 0.0
z0 = [0, 0]
solver.set_initial_value(z0, t0)

# Create the array `t` of time values at which to compute
# the solution, and create an array to hold the solution.
# Put the initial value in the solution array.
t1 = 2.5
N = 75
t = np.linspace(t0, t1, N)
sol = np.empty((N, 2))
sol[0] = z0

# Repeatedly call the `integrate` method to advance the
# solution to time t[k], and save the solution in sol[k].
k = 1
while solver.successful() and solver.t < t1:
    solver.integrate(t[k])
    sol[k] = solver.y
    k += 1

# Plot the solution...
plt.plot(t, sol[:,0], label='x')
plt.plot(t, sol[:,1], label='y')
plt.xlabel('t')
plt.grid(True)
plt.legend()
plt.show()

Answer 1

Your initial state ( z0 ) is [0,0] . The time derivative ( fun ) for this initial state is also [0,0] . Hence, for this initial condition, [0,0] is the correct solution for all times.

If you change your initial condition to some other value, you should observe more interesting result.