lines 7-51 of file: example/utility/ode_err_control.cpp

{xrst_begin ode_err_control.cpp}

OdeErrControl: Example and Test
###############################

Define
:math:`X : \B{R} \rightarrow \B{R}^2` by

.. math::
   :nowrap:

   \begin{eqnarray}
      X_0 (0)       & = & 1  \\
      X_1 (0)       & = & 0  \\
      X_0^{(1)} (t) & = & - \alpha X_0 (t)  \\
      X_1^{(1)} (t) & = &  1 / X_0 (t)
   \end{eqnarray}

It follows that

.. math::
   :nowrap:

   \begin{eqnarray}
   X_0 (t) & = &  \exp ( - \alpha t )  \\
   X_1 (t) & = & [ \exp( \alpha t ) - 1 ] / \alpha
   \end{eqnarray}

This example tests OdeErrControl using the relations above.

Nan
***
Note that :math:`X_0 (t) > 0` for all :math:`t` and that the
ODE goes through a singularity between :math:`X_0 (t) > 0`
and :math:`X_0 (t) < 0`.
If :math:`X_0 (t) < 0`,
we return ``nan`` in order to inform
``OdeErrControl`` that its is taking to large a step.

{xrst_literal
   // BEGIN C++
   // END C++
}

{xrst_end ode_err_control.cpp}