void de ( void f ( double t, double y[], double yp[] ), int neqn, double y[], 
  double &t, double tout, double relerr, double abserr, int &iflag, double yy[], 
  double wt[], double p[], double yp[], double ypout[], double phi[], 
  double alpha[], double beta[], double sig[], double v[], double w[], 
  double g[], bool &phase1, double psi[], double &x, double &h, double &hold, 
  bool &start, double &told, double &delsgn, int &ns, bool &nornd, int &k, int &kold, 
  int &isnold );
int i4_sign ( int i );
void intrp ( double x, double y[], double xout, double yout[], double ypout[], 
  int neqn, int kold, double phi[], double psi[] );
void ode ( void f ( double t, double y[], double yp[] ), int neqn, double y[], 
  double &t, double tout, double relerr, double abserr, int &iflag, 
  double work[], int iwork[] );
double r8_sign ( double x );
void step ( double &x, double y[], void f ( double t, double y[], double yp[] ), 
  int neqn, double &h, double &eps, double wt[], bool &start, double &hold, 
  int &k, int &kold, bool &crash, double phi[], double p[], double yp[], 
  double psi[], double alpha[], double beta[], double sig[], double v[], 
  double w[], double g[], bool &phase1, int &ns, bool &nornd );
void timestamp ( );