.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples_gallery/advanced_pdes/pde_custom_class.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_advanced_pdes_pde_custom_class.py>`
        to download the full example code.

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

.. _sphx_glr_examples_gallery_advanced_pdes_pde_custom_class.py:


Kuramoto-Sivashinsky - Using custom class
=========================================

This example implements a scalar PDE using a custom class. We here consider the
`Kuramoto–Sivashinsky equation
<https://en.wikipedia.org/wiki/Kuramoto–Sivashinsky_equation>`_, which for instance
describes the dynamics of flame fronts:

.. math::
    \partial_t u = -\frac12 |\nabla u|^2 - \nabla^2 u - \nabla^4 u

.. GENERATED FROM PYTHON SOURCE LINES 13-34



.. image-sg:: /examples_gallery/advanced_pdes/images/sphx_glr_pde_custom_class_001.png
   :alt: pde custom class
   :srcset: /examples_gallery/advanced_pdes/images/sphx_glr_pde_custom_class_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 PDEBase, ScalarField, UnitGrid


    class KuramotoSivashinskyPDE(PDEBase):
        """Implementation of the normalized Kuramoto–Sivashinsky equation."""

        def evolution_rate(self, state, t=0):
            """Implement the python version of the evolution equation."""
            state_lap = state.laplace(bc="auto_periodic_neumann")
            state_lap2 = state_lap.laplace(bc="auto_periodic_neumann")
            state_grad = state.gradient(bc="auto_periodic_neumann")
            return -state_grad.to_scalar("squared_sum") / 2 - state_lap - state_lap2


    grid = UnitGrid([32, 32])  # generate grid
    state = ScalarField.random_uniform(grid)  # generate initial condition

    eq = KuramotoSivashinskyPDE()  # define the pde
    result = eq.solve(state, t_range=10, dt=0.01)
    result.plot()


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

   **Total running time of the script:** (0 minutes 0.642 seconds)


.. _sphx_glr_download_examples_gallery_advanced_pdes_pde_custom_class.py:

.. only:: html

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

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

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

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

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

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

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