``braincell.quad`` module
=========================

.. currentmodule:: braincell.quad
.. automodule:: braincell.quad



``braincell.quad`` provides a mechanism to define coupled ordinary differential equations (ODEs)
and solve them using various numerical integration methods.
The integration methods are categorized into exponential integrators, Runge-Kutta methods,
implicit methods, and Diffrax integrators.


Defining Coupled ODEs
---------------------

.. autosummary::
   :toctree: generated/
   :nosignatures:
   :template: classtemplate.rst

    DiffEqState
    DiffEqModule
    IndependentIntegration




Overall Integration Interface
-----------------------------

.. autosummary::
   :toctree: generated/

    get_integrator


Exponential Integrators
------------------------


.. autosummary::
   :toctree: generated/

    exp_euler_step
    ind_exp_euler_step


Runge-Kutta Integrators
-----------------------

.. autosummary::
   :toctree: generated/


    euler_step
    midpoint_step
    rk2_step
    heun2_step
    ralston2_step
    rk3_step
    heun3_step
    ssprk3_step
    ralston3_step
    rk4_step
    ralston4_step


Diffrax Explicit Integrators
-----------------------------

.. autosummary::
   :toctree: generated

    diffrax_euler_step
    diffrax_heun_step
    diffrax_midpoint_step
    diffrax_ralston_step
    diffrax_bosh3_step
    diffrax_tsit5_step
    diffrax_dopri5_step
    diffrax_dopri8_step


Diffrax Implicit Integrators
-----------------------------

.. autosummary::
   :toctree: generated

    diffrax_bwd_euler_step
    diffrax_kvaerno3_step
    diffrax_kvaerno4_step
    diffrax_kvaerno5_step