void CalcFunct      // a function that codes the analytic expression...
                    // ...of the forcing function of the sample problem
                    // it is called only by the function NumericJacob...
                    // ...to estimate the jacobian matrix by finite differences

         (double x_ [],   // argument of the sample forcing function
          int    dim,     // dimension of the sample problem
          double F  []);  // value of of the sample forcing function at x_ []

void CalcFunct (double x_ [], int dim, double F [])
{
  double beta1 = 1.0e+3;
  double beta2 = 1.0e-3;

  if (dim != 2) abort ();

                               // sample problem
                               // dx0 / dt = f0 = (1 - x0) - beta1 x0 x1
                               // dx1 / dt = f1 = -beta2 x0 x1

  F [0] = (1 - x_ [0]) - beta1 * x_ [1] * x_ [0];
  F [1] = -(x_ [1] * x_ [0]) * beta2;
}