void porous_medium_exact ( double x, double t, double &u, double &ut, 
  double &ux, double &uxx );
void porous_medium_parameters ( double *c_in, double *delta_in, double *m_in, 
  double *t0_in, double *tstop_in, double *c_out, double *delta_out, 
  double *m_out, double *t0_out, double *tstop_out );
double porous_medium_residual ( double t, double x );