Wednesday - June 7, 2023

Fortran ~ Bisection Method

Fortran ~ Bisection Method

  • This method is used for finding an approximate solution to an equation f(x)=0 to the desired degree of accuracy. 
  • This method is based on a concept which states that if a function f(x) is continuous in the closed interval a<=x<=b and f(a), f(b) are of opposite signs, 
  • then there must exist at least one real root between x=a and x=b.
  • F(X) =2.0*X**3-5.0*X-2.15
bisection method step by step, bisection method solved examples, bisection method python, bisection method numerical analysis, bisection method matlab, bisection method in c, bisection method example problems with solutions, bisection method example problems with solution pdf, bisection method calculator, bisection method matlab, bisection method python, bisection method khan academy, bisection method table, numericals of bisection method,
Image Source ~ Crafted With ©Ishwaranand – 2020 ~ Image by ©Ishwaranand

Write a program to demonstrate the application of the Bisection method to locate the root of the equation.?

PROGRAM BISECT
C
C        PROGRAM TO LOCATE A ROOT OF EQUATION USING BISECTION METHOD
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 ARITHMETIC MEAN
           XM=(XL+XR)/2.0
           CHK=ABS (F (XM))
C        EXIT LOOP IF ROOT FOUND
          IF (CHK.LE.0.0001) GOTO 200
C        EXIT LOOPS IF UNABLE TO FIND ROOT EVEN AFTER 100+ CYCLES
           IF (I.GT.100) GOTO 300
C        GET NEW LOWER AND UPPER LIMITS FOR 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)
2 4
ROOT FOUNDATION AT X = 2.5815153

Crafted by ISHWARANAND | Distributed by ISHWARANAND

Fortran ~ Regula Falsi Method

Slope Deflection Method

.