C-----SHOOTING METHOD ]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]
      IMPLICIT NONE
      REAL*8 Y0,Z0
      REAL*8 Y1,Y2
      REAL*8 Z1,Z2
      REAL*8 DEL,DF
      INTEGER ITE

      DEL=1.0D-5  

C-----INITIAL VALUE OF DERIVATION AT X=0.0 ]]]]]]]]]]]]]]]]]]]]]]]]]]]]]
      Z0 =0.0D00

C-----MODIFIED SECANT METHOD FOR Z0 VALUE ]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]
      DO ITE=1,5
      Z1=Z0
      CALL RK4(Z1,Y1)
      Z2=Z0+DEL
      CALL RK4(Z2,Y2)

      DF=(Y2-Y1)/DEL
      Z0=Z0-Y1/DF
      WRITE(6,*) "ROOT_Z0=",Z0
      END DO
      END




C-----==================================================================
      SUBROUTINE RK4(Z0,Y0)
C-----==================================================================
C-----FOURTH-RUNGE RUNGE-KUTTA METHOD ]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]
      IMPLICIT NONE
      REAL*8  KY(0:4),KZ(0:4),C(4)
      REAL*8  X0,Y0,Z0
      REAL*8  X1,Y1,Z1
      REAL*8  PI,DX
      INTEGER M,ITE,ITE_MAX

      ITE_MAX=1000
      PI=4.0D00*ATAN(1.0D00)
      DX=PI/DBLE(ITE_MAX)
      C(1)=0.0D00
      C(2)=0.5D00
      C(3)=0.5D00
      C(4)=1.0D00

C-----INITIAL VALUES ]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]
      X0=0.0D00
      Y0=1.0D0
C     Z0=0.0D00
      KY(:)=0.0D00
      KZ(:)=0.0D00

C-----FOURTH-ORDER RUNGE-KUTTA METHOD ]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]
      DO ITE=1,ITE_MAX

C     WRITE(6,*) "ITERATION NUMBER=",ITE
      DO M=1,4
      X1   = X0+C(M)*DX
      Y1   = Y0+C(M)*DX*KY(M-1)
      Z1   = Z0+C(M)*DX*KZ(M-1)
      KY(M)= Z1
      KZ(M)=-3.0D00*X1*Z1-7.0D00*Y1+COS(2.0D00*X1)
      END DO

      X0 = X0 + DX
      Y0 = Y0 + (KY(1)+2D00*KY(2)+2D00*KY(3)+KY(4))/6D00 *DX
      Z0 = Z0 + (KZ(1)+2D00*KZ(2)+2D00*KZ(3)+KZ(4))/6D00 *DX
                  
      WRITE(10,10) X0,Y0,Z0
      END DO 
      WRITE(6 ,11) "X=",X0,"Y=",Y0,"Z=",Z0
      

   10 FORMAT(F12.6,2X,F12.6,2X,F12.6,2X,F12.6)
   11 FORMAT(A2,2X,F10.6,2X,A2,2X,F10.6,2X,A2,2X,F10.6,2X)
      RETURN
      END