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Python binding for odeiv2 in GNU Scientific Library (GSL).

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pygslodeiv2 provides a Python binding to the Ordinary Differential Equation integration routines exposed by the odeiv2 interface of GSL - GNU Scientific Library. The odeiv2 interface allows a user to numerically integrate (systems of) differential equations.

The following stepping functions are available:

  • rk2
  • rk4
  • rkf45
  • rkck
  • rk8pd
  • rk1imp
  • rk2imp
  • rk4imp
  • bsimp
  • msadams
  • msbdf

Note that all implicit steppers (those ending with “imp”) and msbdf require a user supplied callback for calculating the jacobian.

You may also want to know that you can use pygslodeiv2 from pyodesys which can e.g. derive the Jacobian analytically (using SymPy). pyodesys also provides plotting functions, C++ code-generation and more.


Autogenerated API documentation for latest stable release is found here: (and the development version for the current master branch are found here:


Simplest way to install is to use the conda package manager:

$ conda install -c bjodah pygslodeiv2 pytest
$ python -m pytest --pyargs pygslodeiv2

tests should pass.

Binary distribution is available here:, conda recipes for stable releases are available here:

Source distribution is available here (requires GSL v1.16 or v2.1 shared lib with headers): (with mirrored files kept here:


The classic van der Pol oscillator (see examples/

>>> import numpy as np
>>> from pygslodeiv2 import integrate_predefined  # also: integrate_adaptive
>>> mu = 1.0
>>> def f(t, y, dydt):
...     dydt[0] = y[1]
...     dydt[1] = -y[0] + mu*y[1]*(1 - y[0]**2)
>>> def j(t, y, Jmat, dfdt):
...     Jmat[0, 0] = 0
...     Jmat[0, 1] = 1
...     Jmat[1, 0] = -1 -mu*2*y[1]*y[0]
...     Jmat[1, 1] = mu*(1 - y[0]**2)
...     dfdt[0] = 0
...     dfdt[1] = 0
>>> y0 = [1, 0]; dt0=1e-8; t0=0.0; atol=1e-8; rtol=1e-8
>>> tout = np.linspace(0, 10.0, 200)
>>> yout, info = integrate_predefined(f, j, y0, tout, dt0, atol, rtol,
...                                   method='bsimp')  # Implicit Bulirsch-Stoer
>>> import matplotlib.pyplot as plt
>>> series = plt.plot(tout, yout)
>>>  # doctest: +SKIP

For more examples see examples/, and rendered jupyter notebooks here:


The source code is Open Source and is released under GNU GPL v3. See LICENSE for further details. Contributors are welcome to suggest improvements at


Björn I. Dahlgren, contact:

  • gmail address: bjodah

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