.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples_gallery/simple.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_examples_gallery_simple.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_examples_gallery_simple.py:


Simple diffusion equation
=========================

This example solves a simple diffusion equation in two dimensions.

.. GENERATED FROM PYTHON SOURCE LINES 7-16



.. image-sg:: /examples_gallery/images/sphx_glr_simple_001.png
   :alt: simple
   :srcset: /examples_gallery/images/sphx_glr_simple_001.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none


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|

.. code-block:: Python


    from pde import DiffusionPDE, ScalarField, UnitGrid

    grid = UnitGrid([64, 64])  # generate grid
    state = ScalarField.random_uniform(grid, 0.2, 0.3)  # generate initial condition

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


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 9.469 seconds)


.. _sphx_glr_download_examples_gallery_simple.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: simple.ipynb <simple.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: simple.py <simple.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: simple.zip <simple.zip>`