odeint from scipy.integrate in Python giving wrong result?

Question

I am trying to solve the ivp y'=-y-5 * exp(-t) * sin(5 t), y(0)=1, using the following code:

%pylab inline
%matplotlib inline
from scipy.integrate import odeint

def mif(t, y):
    return -y-5*exp(-t)*sin(5*t)

tspan = np.arange(0, 3, 0.000001)
y0 = 1.0
y_result = odeint(mif, y0, tspan)
y_result = y_result[:, 0]  # convert the returned 2D array to a 1D array
plt.figure()
plt.plot(tspan, y_result)
plt.show()

However, the plot I get is wrong, it does not match what I obtain, say, with Matlab or Mathematica. It is actually different from the following alternative integration:

from scipy.integrate import ode

# initialize the 4th order Runge-Kutta solver
solver = ode(mif).set_integrator('dop853')

# initial value
y0 = 1.0
solver.set_initial_value(y0, 0)

values = 1000
t = np.linspace(0.0001, 3, values)
y = np.zeros(values)

for ii in range(values):
    y[ii] = solver.integrate(t[ii])[0] #z[0]=u

which does yield correct result. What am I doing wrong with the odeint?

wrdeman · Accepted Answer · 2015-02-28 11:25:40Z

4

The function arguments change between ode and odeint. For odeint you need

def mif(y, t):

and for ode

def mif(t, y):

e.g.

%pylab inline
%matplotlib inline
from scipy.integrate import odeint

def mif(t,y):
    return y

tspan = np.arange(0, 3, 0.000001)
y0 = 0.0
y_result = odeint(mif, y0, tspan)
plt.figure()
plt.plot(tspan, y_result)
plt.show()

and

from scipy.integrate import ode

def mif(y, t):
    return y

# initialize the 4th order Runge-Kutta solver
solver = ode(mif).set_integrator('dop853')

# initial value
y0 = 0.000000
solver.set_initial_value([y0], 0.0)

values = 1000
t = np.linspace(0.0000001, 3, values)
y = np.zeros(values)

for ii in range(values):
    y[ii] = solver.integrate(t[ii]) #z[0]=u
plt.figure()
plt.plot(t, y)
plt.show()

answered Feb 28, 2015 at 11:25

wrdeman

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