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

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

.. _sphx_glr_examples_gallery_advanced_pdes_stratonovich.py:


SDE with Stratonovich interpretation
====================================

This example solves a stochastic diffusion equation with Stratonovich interpretation

.. GENERATED FROM PYTHON SOURCE LINES 7-39



.. image-sg:: /examples_gallery/advanced_pdes/images/sphx_glr_stratonovich_001.png
   :alt: stratonovich
   :srcset: /examples_gallery/advanced_pdes/images/sphx_glr_stratonovich_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 PDE, ScalarField, UnitGrid


    class AllenCahnNoisePDE(PDE):
        """Allen–Cahn PDE with custom noise implementation."""

        use_noise_variance = True

        def make_noise_variance(self, state, *, backend, ret_diff=False):
            """Make function that calculates noise variance."""
            noise = float(self.noise)

            if ret_diff:

                def noise_variance(state_data, t):
                    return noise * state_data**2, 2 * noise * state_data

            else:

                def noise_variance(state_data, t):
                    return noise * state_data**2

            return noise_variance


    eq = AllenCahnNoisePDE(
        rhs={"c": "laplace(c) + c - c**3"}, noise=1.0, noise_interpretation="stratonovich"
    )
    state = ScalarField.random_uniform(UnitGrid([64, 64]), -1, 1)
    result = eq.solve(state, t_range=10, dt=1e-3, solver="milstein")
    result.plot()


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

   **Total running time of the script:** (0 minutes 5.652 seconds)


.. _sphx_glr_download_examples_gallery_advanced_pdes_stratonovich.py:

.. only:: html

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

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

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

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

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

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

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