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

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

.. _sphx_glr_examples_gallery_advanced_pdes_solver_comparison.py:


Solver comparison
=================

This example shows how to set up solvers explicitly and how to extract
diagnostic information.

.. GENERATED FROM PYTHON SOURCE LINES 8-48



.. image-sg:: /examples_gallery/advanced_pdes/images/sphx_glr_solver_comparison_001.png
   :alt: Deviation: 7.3e-09, 8.4e-09, explicit solver, explicit, adaptive solver, scipy solver
   :srcset: /examples_gallery/advanced_pdes/images/sphx_glr_solver_comparison_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    Diagnostic information from first run:
    {'controller': {'mpi_run': False, 't_start': 0, 't_end': 1.0, 'profiler': {'solver': 0.0053741849999937585, 'tracker': 3.612999999802469e-05, 'compilation': 8.759453668000006}, 'jit_count': {'make_stepper': 10, 'simulation': 0}, 'solver_start': '2025-05-24 15:38:14.440164', 'successful': True, 'stop_reason': 'Reached final time', 'solver_duration': '0:00:00.005405', 't_final': 1.0}, 'package_version': 'unknown', 'solver': {'class': 'ExplicitSolver', 'pde_class': 'DiffusionPDE', 'scheme': 'euler', 'backend': 'numba', 'dt': 0.001, 'steps': 1000, 'post_step_data': None, 'stochastic': np.False_}}

    Diagnostic information from second run:
    {'controller': {'mpi_run': False, 't_start': 0, 't_end': 1.0, 'profiler': {'solver': 0.08682866699999181, 'tracker': 3.581000001418033e-05, 'compilation': 2.266394313999996}, 'jit_count': {'make_stepper': 1, 'simulation': 0}, 'solver_start': '2025-05-24 15:38:16.713157', 'successful': True, 'stop_reason': 'Reached final time', 'solver_duration': '0:00:00.087096', 't_final': np.float64(1.0)}, 'package_version': 'unknown', 'solver': {'class': 'ExplicitSolver', 'pde_class': 'DiffusionPDE', 'dt_statistics': {'min': 0.001, 'max': 0.1690822072051333, 'mean': 0.08333333333333333, 'std': 0.051707546359477996, 'count': 12.0}, 'scheme': 'runge-kutta', 'backend': 'numba', 'dt': 0.001, 'dt_adaptive': True, 'steps': 12, 'stochastic': np.False_, 'post_step_data': None}}

    Diagnostic information from third run:
    {'controller': {'mpi_run': False, 't_start': 0, 't_end': 1.0, 'profiler': {'solver': 0.0012670910000025515, 'tracker': 3.288000000623015e-05, 'compilation': 1.9059541359999912}, 'jit_count': {'make_stepper': 1, 'simulation': 0}, 'solver_start': '2025-05-24 15:38:19.490997', 'successful': True, 'stop_reason': 'Reached final time', 'solver_duration': '0:00:00.001294', 't_final': np.float64(1.0)}, 'package_version': 'unknown', 'solver': {'class': 'ScipySolver', 'pde_class': 'DiffusionPDE', 'dt': None, 'steps': 50, 'stochastic': False, 'backend': 'numba'}}







|

.. code-block:: Python


    import pde

    # initialize the grid, an initial condition, and the PDE
    grid = pde.UnitGrid([32, 32])
    field = pde.ScalarField.random_uniform(grid, -1, 1)
    eq = pde.DiffusionPDE()

    # try the explicit solver
    solver1 = pde.ExplicitSolver(eq)
    controller1 = pde.Controller(solver1, t_range=1, tracker=None)
    sol1 = controller1.run(field, dt=1e-3)
    sol1.label = "explicit solver"
    print("Diagnostic information from first run:")
    print(controller1.diagnostics)
    print()

    # try an explicit solver with adaptive time steps
    solver2 = pde.ExplicitSolver(eq, scheme="runge-kutta", adaptive=True)
    controller2 = pde.Controller(solver2, t_range=1, tracker=None)
    sol2 = controller2.run(field, dt=1e-3)
    sol2.label = "explicit, adaptive solver"
    print("Diagnostic information from second run:")
    print(controller2.diagnostics)
    print()

    # try the standard scipy solver
    solver3 = pde.ScipySolver(eq)
    controller3 = pde.Controller(solver3, t_range=1, tracker=None)
    sol3 = controller3.run(field)
    sol3.label = "scipy solver"
    print("Diagnostic information from third run:")
    print(controller3.diagnostics)
    print()

    # plot both fields and give the deviation as the title
    deviation12 = ((sol1 - sol2) ** 2).average
    deviation13 = ((sol1 - sol3) ** 2).average
    title = f"Deviation: {deviation12:.2g}, {deviation13:.2g}"
    pde.FieldCollection([sol1, sol2, sol3]).plot(title=title)


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

   **Total running time of the script:** (0 minutes 14.059 seconds)


.. _sphx_glr_download_examples_gallery_advanced_pdes_solver_comparison.py:

.. only:: html

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

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

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

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

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

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

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