Using adaptive step sizes with scipy.integrate.ode

Question

The (brief) documentation for scipy.integrate.ode says that two methods (dopri5 and dop853) have stepsize control and dense output. L

Answer 1

The integrate method accepts a boolean argument step that tells the method to return a single internal step. However, it appears that the 'dopri5' and 'dop853' solvers do not support it.

The following code shows how you can get the internal steps taken by the solver when the 'vode' solver is used:

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


def logistic(t, y, r):
    return r * y * (1.0 - y)

r = .01

t0 = 0
y0 = 1e-5
t1 = 5000.0

backend = 'vode'
#backend = 'dopri5'
#backend = 'dop853'
solver = ode(logistic).set_integrator(backend)
solver.set_initial_value(y0, t0).set_f_params(r)

sol = []
while solver.successful() and solver.t < t1:
    solver.integrate(t1, step=True)
    sol.append([solver.t, solver.y])

sol = np.array(sol)

plt.plot(sol[:,0], sol[:,1], 'b.-')
plt.show()

Result: