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

.. only:: html

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

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

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

.. _sphx_glr__build_auto_examples_convergence_SelectedRungeKutta.py:


Convergence analysis of Runge-Kutta methods for ODE IVP
=======================================================

.. GENERATED FROM PYTHON SOURCE LINES 7-8

Evaluation of relative quadrature error with the following parameters:

.. GENERATED FROM PYTHON SOURCE LINES 8-42

.. code-block:: Python



    eq_names = [
        "y'' = -y"          ,
        "y'' = - exp(y)"    ,
        "y'' = xy"          ,
        "y' = Az; z' = By"  ,
    ]

    implicit_methods = {
        f'{rk_name} {order}' : choreo.scipy_plus.multiprec_tables.ComputeImplicitSymplecticRKTablePair_Gauss(order,method=rk_name) for rk_name, order in itertools.product(["Gauss"], [2,4,6,8])
        # f'{rk_name} {order}' : choreo.scipy_plus.multiprec_tables.ComputeImplicitSymplecticRKTablePair_Gauss(order, method=rk_name) for rk_name, order in itertools.product(["Radau_IIA"], [2,3,4,5])
    }

    explicit_methods = {
        rk_name : getattr(globals()['precomputed_tables'], rk_name) for rk_name in [
                'McAte4'    ,
                'McAte5'    ,
                'KahanLi8'  ,
                'SofSpa10'  ,
        ]
    }

    scipy_methods = [
        "RK45" ,  
        "RK23" ,  
        "DOP853" ,  
        "Radau" ,  
        "BDF" ,  
        "LSODA" ,  
    ]










.. GENERATED FROM PYTHON SOURCE LINES 145-146

The following plots give the measured relative error as a function of the number of quadrature subintervals

.. GENERATED FROM PYTHON SOURCE LINES 146-150

.. code-block:: Python



    plt.show()




.. image-sg:: /_build/auto_examples/convergence/images/sphx_glr_SelectedRungeKutta_001.png
   :alt: Relative error on integrand y'' = -y, Relative error on integrand y'' = - exp(y), Relative error on integrand y'' = xy, Relative error on integrand y' = Az; z' = By
   :srcset: /_build/auto_examples/convergence/images/sphx_glr_SelectedRungeKutta_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 197-198

Error as a function of running time

.. GENERATED FROM PYTHON SOURCE LINES 198-203

.. code-block:: Python



    plt.show()





.. image-sg:: /_build/auto_examples/convergence/images/sphx_glr_SelectedRungeKutta_002.png
   :alt: Relative error as a function of computational cost for equation y'' = -y, Relative error as a function of computational cost for equation y'' = - exp(y), Relative error as a function of computational cost for equation y'' = xy, Relative error as a function of computational cost for equation y' = Az; z' = By
   :srcset: /_build/auto_examples/convergence/images/sphx_glr_SelectedRungeKutta_002.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 2.815 seconds)


.. _sphx_glr_download__build_auto_examples_convergence_SelectedRungeKutta.py:

.. only:: html

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

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

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

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

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


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_