ODES is a scikit for Python 3.6-3.9 offering extra ode/dae solvers, as an extension to what is available in scipy. The documentation is available at Read The Docs, and API docs can be found at https://bmcage.github.io/odes.

ODES provides interfaces to the following solvers:

• BDF linear multistep method for stiff problems (CVODE and IDA from SUNDIALS)
• Adams-Moulton linear multistep method for nonstiff problems (CVODE and IDA from SUNDIALS)
• Explicit Runge-Kutta method of order (4)5 with stepsize control ( dopri5 from scipy.integrate)
• Explicit Runge-Kutta method of order 8(5,3) with stepsize control ( dop853 from scipy.integrate)
• Historical solvers: lsodi and ddaspk are available for comparison reasons. Use IDA instead! Note that lsodi fails on architecture aarch64.

A simple example solving the Van der Pol oscillator is as follows:

import matplotlib.pyplot as plt
import numpy as np
from scikits.odes import ode

t0, y0 = 1, np.array([0.5, 0.5])  # initial condition
def van_der_pol(t, y, ydot):
    """ we create rhs equations for the problem"""
    ydot[0] = y[1]
    ydot[1] = 1000*(1.0-y[0]**2)*y[1]-y[0]

solution = ode('cvode', van_der_pol, old_api=False).solve(np.linspace(t0,500,200), y0)
plt.plot(solution.values.t, solution.values.y[:,0], label='Van der Pol oscillator')
plt.show()

For simplicity there is also a convenience function odeint wrapping the ode solver class. See the User Guide for a simple example for odeint, as well as simple examples for object orientated interfaces and further examples using ODES solvers.

You can learn by example from following code that uses ODES:

• Centrifuge simulation, a wrapper around the ida solver: see centrifuge-1d

You have a project using odes? Do a pull request to add your project.

If you use ODES as part of your research, can you please cite the ODES JOSS paper. Additionally, if you use one of the SUNDIALS solvers, we strongly encourage you to cite the SUNDIALS papers.