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  void kkabg(n,x,t,a,b,c,y) 
  int n; 
  double x[],t,a,b,c,y[]; 
  { int i; 
    double s1,ss,v1,vv,a1,aa; 
    aa=0.0; vv=0.0;ss=0.0; 
    for (i=0; i<=n-1; i++) 
      { s1=ss+t*vv+t*t*aa/2.0; 
        v1=vv+t*aa; a1=aa; 
        ss=s1+a*(x[i]-s1); y[i]=ss; 
        vv=v1+b*(x[i]-s1); 
        aa=a1+2.0*c*(x[i]-s1)/(t*t); 
      } 
    return; 
  }