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

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

.. _sphx_glr_examples_gallery_simple_pdes_klein_gordon.py:


Klein-Gordon equation
=====================

This example solves the Klein-Gordon equation in one dimension, showing the
effect of the mass term on wave propagation.  With mass=0 the equation reduces
to the standard wave equation; increasing the mass introduces dispersion.

.. GENERATED FROM PYTHON SOURCE LINES 9-19



.. image-sg:: /examples_gallery/simple_pdes/images/sphx_glr_klein_gordon_001.png
   :alt: klein gordon
   :srcset: /examples_gallery/simple_pdes/images/sphx_glr_klein_gordon_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 KleinGordonPDE, ScalarField, UnitGrid

    grid = UnitGrid([128])  # generate grid
    u = ScalarField.from_expression(grid, "exp(-((x - 32) / 5) ** 2)")

    eq = KleinGordonPDE(speed=1, mass=0.5)  # define the pde
    state = eq.get_initial_condition(u)
    result = eq.solve(state, t_range=50, dt=0.01)
    result[0].plot()


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

   **Total running time of the script:** (0 minutes 2.686 seconds)


.. _sphx_glr_download_examples_gallery_simple_pdes_klein_gordon.py:

.. only:: html

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

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

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

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

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

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

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