void mad_compute ( void f ( double t, double y[], double dydt[] ), double t0, 
  double tmax, int m, double y0[], double tau0, double reltol, double abstol, 
  int nmax, int &nstep, int &n_rejected, int &n_fsolve, double t[], double y[] );
void mad_lte ( int m, double y[], double tau[], double reltol, double abstol, 
  double &tnmin, double &tnmax );
void mad_phase_plot ( int n, int m, double t[], double y[], string label );
void mad_solution_plot ( int n, int m, double t[], double y[], string label );
void mad_stats ( int n, int n_rejected, int n_fsolve, double t[] );
void mad_step ( int m, double to, double yo[], double tauo, 
  void f ( double t, double y[], double dydt[] ), double theta, double tol, 
  double &tn, double yn[], bool &fsolve_fail );
void mad_timestep_plot ( int n, double t[], string label );