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lines 7-46 of file: example/general/ode_stiff.cpp
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{xrst_begin ode_stiff.cpp}
{xrst_spell
   rosen
}

A Stiff Ode: 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^\prime (t) & = & - a_0 x_0 (t) \\
      x_1^\prime (t) & = & + a_0 x_0 (t) - a_1 x_1 (t)
   \end{eqnarray}

If :math:`a_0 \gg a_1 > 0`, this is a stiff Ode and
the analytic solution is

.. math::
   :nowrap:

   \begin{eqnarray}
   x_0 (t)    & = & \exp( - a_0 t ) \\
   x_1 (t)    & = & a_0 [ \exp( - a_1 t ) - \exp( - a_0 t ) ] / ( a_0 - a_1 )
   \end{eqnarray}

The example tests Rosen34 using the relations above:

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

{xrst_end ode_stiff.cpp}