Problems
========

Simple problem
--------------

.. doxygenclass:: ponio::simple_problem
   :project: solver
   :members:

.. doxygenfunction:: ponio::make_simple_problem
   :project: solver


Lawson problem
--------------

.. doxygenclass:: ponio::lawson_problem
   :project: solver
   :members:

.. doxygenfunction:: ponio::make_lawson_problem
   :project: solver


Implicit problem
----------------

This kind of problems are defined by a function and its Jacobian.

.. doxygenclass:: ponio::implicit_problem
   :project: solver
   :members:

.. doxygenfunction:: ponio::make_implicit_problem
   :project: solver


Implicit problem with operator
------------------------------

This kind of problems are defined by a function and an operator, for example to solve :

.. maths::

  \dot{u} = f(t, u)

- the function is :math:`f` ;
- the operator is :math:`t \mapsto f(t, \cdot)` which is a function.

.. doxygenclass:: ponio::implicit_operator_problem
   :project: solver
   :members:

.. doxygenfunction:: ponio::make_implicit_operator_problem
   :project: solver


Problem
-------

A problem is a collection of sub-problems defined by previous problems.

.. doxygenclass:: ponio::problem
   :project: solver
   :members: