c**************************************************
      SUBROUTINE NEWTON (x0,er,nmax,xr,ea,fr)
c**************************************************
c     Routs of a nonlinear function FF
c     Newton-Raphson method 
c
      IMPLICIT REAL*8 (a-h, o-z)
c
c-- initial values
      niter=0
      xold=x0
      fr=FF(xold)
c
c___ start of iterations _______________
c
      write(*,*) '  niter   xr   ea   fr '
      DO
         niter=niter+1
         fgr=FD1(xold)
         IF(fgr .NE. 0.) THEN
            xr=xold-fr/fgr
         ELSE
            WRITE(*,*) 'error!  zero derivative'
            RETURN
         ENDIF
c-- xr is a roote?
         fr=FF(xr)
         if(fr. EQ. 0.) THEN
            ea=0.
            EXIT
         ENDIF
c-- relative (or absolute) error
         IF (xr .NE. 0.) THEN
            ea=ABS((xr-xold)/xr)
         ELSE
            ea=ABS(xr-xold)
         ENDIF
c-- monitoring (optional)
         WRITE(*,901) niter,xr,ea,fr
c-- exit checks
         IF (ea .LE. er)  EXIT
         IF (niter .GE. nmax)  THEN
            WRITE(*,*) 'warning!  iterations limit'
            EXIT
         ENDIF
         xold=xr
      END DO
      RETURN
 901  FORMAT(2X,I4,E20.10,2E20.6)
      END