Luca Thiede - 1 month ago 17
Python Question

# What am I doing wrong in this Dopri5 implementation

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

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

\$\dot{y} = -y-x^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()


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.