double *doughnut_exact ( int nt, double t[] );
void doughnut_parameters ( 
  double *m_in,  double *n_in,  double *t0_in,  double *y0_in,  double *tstop_in, 
  double *m_out, double *n_out, double *t0_out, double *y0_out, double *tstop_out );