py-pde is a Python package for solving partial differential equations (PDEs). The package provides classes for grids on which scalar and tensor fields can be defined. The associated differential operators are computed using a numba-compiled implementation of finite differences. This allows defining, inspecting, and solving typical PDEs that appear for instance in the study of dynamical systems in physics. The focus of the package lies on easy usage to explore the behavior of PDEs. However, core computations can be compiled transparently using numba for speed.

Try it online!

py-pde is available on pypi, so you should be able to install it through pip:

pip install py-pde

In order to have all features of the package available, you might want to install the following optional packages:

pip install h5py pandas mpi4py numba-mpi

Moreover, ffmpeg needs to be installed for creating movies.

As an alternative, you can install py-pde through conda using the conda-forge channel:

conda install -c conda-forge py-pde

Installation with conda includes all dependencies of py-pde.

A simple example showing the evolution of the diffusion equation in 2d:

import pde

grid = pde.UnitGrid([64, 64])                 # generate grid
state = pde.ScalarField.random_uniform(grid)  # generate initial condition

eq = pde.DiffusionPDE(diffusivity=0.1)        # define the pde
result = eq.solve(state, t_range=10)          # solve the pde
result.plot()                                 # plot the resulting field

PDEs can also be specified by simply writing expressions of the evolution rate. For instance, the Cahn-Hilliard equation can be implemented as

eq = pde.PDE({'c': 'laplace(c**3 - c - laplace(c))'})

which can be used in place of the DiffusionPDE in the example above.

• Tutorial notebooks in the tutorials folder
• Examples gallery with an overview of the capabilities of the package
• The Discussions on GitHub
• Full documentation on readthedocs or as a single PDF file.
• The paper published in the Journal of Open Source Software
• Practical tutorial on pattern formation in biological cells