## Fortran ~ Newton Raphson Method

## 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

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