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lines 7-42 of file: example/utility/ode_err_maxabs.cpp
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{xrst_begin ode_err_maxabs.cpp}

OdeErrControl: Example and Test Using Maxabs Argument
#####################################################

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

.. math::
   :nowrap:

   \begin{eqnarray}
   X_0 (t) & = &  - \exp ( - w_0 t )  \\
   X_1 (t) & = & \frac{w_0}{w_1 - w_0} [ \exp ( - w_0 t ) - \exp( - w_1 t )]
   \end{eqnarray}

It follows that :math:`X_0 (0) = 1`, :math:`X_1 (0) = 0` and

.. math::
   :nowrap:

   \begin{eqnarray}
      X_0^{(1)} (t) & = & - w_0 X_0 (t)  \\
      X_1^{(1)} (t) & = & + w_0 X_0 (t) - w_1 X_1 (t)
   \end{eqnarray}

Note that :math:`X_1 (0)` is zero an if :math:`w_0 t` is large,
:math:`X_0 (t)` is near zero.
This example tests OdeErrControl using the *maxabs* argument.

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

{xrst_end ode_err_maxabs.cpp}