1. Getting started
The py-pde package is developed for python 3.8 and has been tested up to version 3.11 under Linux, Windows, and macOS. Before you can start using the package, you need to install it using one of the following methods.
1.1. Install using pip
The package is available on pypi, so you should be able to install it by running
pip install py-pde
In order to have all features of the package available, you might also want to install the following optional packages:
pip install h5py pandas pyfftw tqdm
Moreover, ffmpeg needs to be installed and for creating movies.
1.2. Install using conda
The py-pde package is also available on conda using the conda-forge channel. You can thus install it using
conda install -c conda-forge py-pde
This installation includes many dependencies to have most features of py-pde.
1.3. Install from source
Installing from source can be necessary if the pypi installation does not work or if the latest source code should be installed from github.
1.3.1. Required prerequisites
The code builds on other python packages, which need to be installed for py-pde to function properly. The required packages are listed in the table below:
Just-in-time compilation to accelerate numerics
Handling numerical data
Miscellaneous scientific functions
Dealing with user-defined mathematical expressions
Display progress bars during calculations
The simplest way to install these packages is to use the
requirements.txt in the base folder:
pip install -r requirements.txt
Alternatively, these package can be installed via your operating system’s package manager, e.g. using macports, homebrew, or conda. The package versions given above are minimal requirements, although this is not tested systematically. Generally, it should help to install the latest version of the package.
1.3.2. Optional packages
The following packages should be installed to use some miscellaneous features:
Storing data in the hierarchical file format
Jupyter notebook support
Parallel processing using MPI
Displaying images interactively
Parallel processing using MPI+numba
Handling tabular data
Faster Fourier transforms
Numba-compiled fast Fourier transforms
For making movies, the ffmpeg should be available.
Additional packages might be required for running the tests in the folder
tests and to build the documentation in the folder
These packages are listed in the files
requirements.txt in the
1.3.3. Downloading py-pde
The package can be simply checked out from
To import the package from any python session, it might be convenient to include
the root folder of the package into the
PYTHONPATH environment variable.
This documentation can be built by calling the make html in the
The final documentation will be available in
Note that a LaTeX documentation can be build using make latexpdf.
1.4. Package overview
The main aim of the
pde package is to simulate partial differential
equations in simple geometries.
Here, the time evolution of a PDE is determined using the method of lines by
explicitly discretizing space using fixed grids.
The differential operators are implemented using the finite difference method.
For simplicity, we consider only regular, orthogonal grids, where each axis has
a uniform discretization and all axes are (locally) orthogonal.
Currently, we support simulations on
with and without periodic boundaries where applicable.
Fields are defined by specifying values at the grid points using the classes
These classes provide methods for applying differential operators to the fields,
e.g., the result of applying the Laplacian to a scalar field is returned by
calling the method
returns another instance of
gradient() returns a
Combining these functions with ordinary arithmetics on fields allows to
represent the right hand side of many partial differential equations that appear
Importantly, the differential operators work with flexible boundary conditions.
The PDEs to solve are represented as a separate class inheriting from
One example defined in this package is the diffusion equation implemented as
DiffusionPDE, but more specific situations need to
be implemented by the user.
Most notably, PDEs can be specified by their expression using the convenient
The PDEs are solved using solver classes, where a simple explicit solver is
ExplicitSolver, but more advanced
implementations can be done.
To obtain more details during the simulation, trackers can be attached to the
solver instance, which analyze intermediate states periodically. Typical
ProgressTracker (display simulation progress),
PlotTracker (display images of the simulation),
SteadyStateTracker (aborting simulation when
a stationary state is reached).
Others can be found in the
Moreover, we provide
FileStorage, which can be used as trackers
to store the intermediate state to memory and to a file, respectively.