This is the oldest method for finding the real root of the equation f(x)=0. This method is similar to the bisection method.
Write a program to demonstrate the calculation of the root of an equation using Regula-Falsi Method.?
PROGRAM RFALSI
C PROGRAM TO LOCATE THE ROOT OF AN EQUATION USING THE METHOD OF FALSE
C POSITION(Regula Falsi)
C
C GIVEN EQUATION
F(X)=2.0*X**3-5.0*X-2.15
C
100 WRITE(*,*)'ENTER YOUR ESTIMATE OF ROOT(LOWER LIMIT, UPPER LIMIT)'
READ(*,*)XL,XR
C FIND IF ESTIMATES ARE CORRECT
CHK=F(XL)*F(XR)
C ENTER DATA AGAIN IF ESTIMATES DO NOT BRACKET THE ROOT
IF(CHK.GT.0.0)GOTO 100
I=0
400 I=I+1
C FIND ROOT POSITION USING GEOMETRIC MEAN
XM=(XR*F(XL)-XL*F(XR))/(F(XL)-F(XR))
CHK=ABS(F(XM))
C EXIT LOOP IF ROOT FOUND
IF(CHK.LE.0.0001)GOTO 200
C EXIT LOOP IF UNABLE TO FIND ROOT EVEN AFTER 100+ CYCLES
IF(I.GT.100)GOTO 300
C GET NEW LOWER AND UPPER LIMITS FOR THE NEXT CYCLE
CHK=F(XL)*F(XM)
IF(CHK.LT.0.0)THEN
XR=XM
ELSE
XL=XM
ENDIF
C START NEXT CYCLE
GOTO 400
200 WRITE (*,*)'ROOT FOUND AT X=', XM
STOP
300 WRITE(*,*)'ROOT NOT FOUND.PROGRAM TERMINATED.'
STOP
END
#OUTPUT
ENTER YOUR ESTIMATE OF ROOT(LOWER LIMIT, UPPER LIMIT)
1 2
ROOT FOUND AT X = 1.4141974
