Fortran ~ Newton Raphson Method

• Let Xo be an approximate value of the root of the equation f(X)=0 either algebraic or transcendental and let h be a real number sufficiently small.
• F(X)=2*X**3-5.0*X-2.15
• This is known as the Newton – Raphson formula or Newton’s iteration formula.

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Write a program to demonstrate the application of the Newton-Raphson method to find the root of the equation.?

PROGRAM RAPHSN
C
C      PROGRAM TO LOCATE A ROOT OF EQUATION USING NEWTON RAPHSON METHOD
C
C      GIVEN EQUATION
         F(X)=2*X**3-5.0*X-2.15
C      DERIVATIVE OF GIVEN EQUATION
         FD(X)=6.0*X**2-5.0
C
         WRITE(*,*)’ENTER YOUR ESTIMATE OF ROOT…’
         READ(*,*)X
          I=0
300    I=I+1
C       FIND ROOT POSITION
           X=X-F(X)/FD(X)
          CHK=ABS(F(X))
C        EXIT LOOP IF ROOT FOUND
           IF(CHK.LE.0.0001)GOTO 100
C        EXIT LOOP IF UNABLE TO FIND ROOT EVEN AFTER 100+CYCLES
          IF(I.GT.100)GOTO 200
C        START NEXT CYCLE
           GOTO 300
100     WRITE(*,*)’ROOT FOUND AT’, X
           STOP
200     WRITE(*,*)’ROOT NOT FOUND’
           STOP
           END

#OUTPUT
ENTER YOUR ESTIMATE OF ROOT
1
ROOT FOUND AT 1.3247180