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UNDERSTANDING BISECTION METHOD USING FORTRAN
Posted Date: 12 Mar 2008 Resource Type: Articles/Knowledge Sharing Category: Computer & Technology
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Posted By: ashish singh Member Level: Diamond
Rating:  Points: 4
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BISECTION METHOD
Bisection Method is very simple and convenient method for solving all types of Algebric and Transcendental Equation.
Let us suppose the equation to be solved be f(x) =0. This is the general form of the equation. Here we have to find the value of x for which f(x) becomes zero. To understand the bisection method first of all we consider any two arbitrary point x1 & x2 such that f(x1) & f(x2) opposite signs. Clearly the solution will be in the range x1-x2. To find the next approximation in the method we get the middle most point of the interval given by m=(x1+x2)/2. If f(m)~0 then m is the solution otherwise the sign of f(m) is compared with the sign of f(x2). If the sign of both is same then x1 is shifted to m otherwise x2 is shifted to m. By this the range is reduced the earlier range by half. This process is evaluating the middle point, comparing the sign of f(m) with f(x1) ….etc. is repeated until we get f(m)~0. This value of m is the solution of given Equation. For example
Fortran Programs for Bisection Method:
C SOLUTION OF BISECTION METHOD
FUNCTION F(X)
F=2*X*X-4*X+1
RETURN
END
2 WRITE(*,*)'ENTER TWO NUMBERS'
READ(*,*) X1,X2
IF(F(X1)*F(X2)) 3,4,2
4 IF(F(X1).EQ.0) THEN
WRITE(*,*)'SOLUTION=',X1
ELSE
WRITE(*,*)'SOLUTION=',X2
ENDIF
3 WRITE(*,*)'ENTER TOL'
READ(*,*) TOL
5 AM=(X1+X2)/2
Y=F(AM)
IF(ABS(Y).LE.TOL) THEN
WRITE(*,*)'SOLUTION=',AM
STOP
ELSE
IF(Y*F(X1).GT.0) THEN
X1=AM
ELSE
X2=AM
ENDIF
ENDIF
GO TO 5
END
Output
BISEC.FOR
Microsoft (R) Segmented-Executable Linker Version 5.15
Copyright (C) Microsoft Corp 1984-1991. All rights reserved.
Object Modules [.OBJ]: BISEC.OBJ
Run File [BISEC.exe]: BISEC.EXE
List File [NUL.MAP]: NUL
Libraries [.LIB]:
Definitions File [NUL.DEF]: ;
D:\FORTRAN\BINB>BISEC
ENTER TWO NUMBERS
2
3
ENTER TWO NUMBERS
2
1
ENTER TOL
.005
SOLUTION= 1.707031
Stop - Program terminated.
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