void f_exact ( double z, double *f, double *fz, double *fzz );
double f_residual ( double f, double fz, double fzz );
void fisher_exact ( double t, double x, double *u, double *ut, double *ux, 
  double *uxx );
void fisher_parameters ( double *a_in, double *c_in, double *k_in, 
  double *a_out, double *c_out, double *k_out );
double fisher_residual ( double t, double x );