Bisection method in numerical analysis implementation using perl language

This video is about to implementation of Bisection method using Perl language..

Bisection method -----------

Bisection method is the simplest among all the numerical schemes to solve the transcendental equations. This scheme is based on the intermediate value theorem for continuous functions .
Consider a transcendental equation f (x) = 0 which has a zero in the interval (a,b) and f (a) * f (b) is less than 0. Bisection scheme computes the zero, say c, by repeatedly halving the interval (a,b). That is, starting with

c = (a+b) / 2
the interval (a,b) is replaced either with (c,b) or with (a,c) depending on the sign of f (a) * f (c) . This process is continued until the zero is obtained. Since the zero is obtained numerically the value of c may not exactly match with all the decimal places of the analytical solution of f (x) = 0 in the interval (a,b).

Bisection Algorithm--------

An algorithm could be defined as follows. Suppose we need a root for
f (x) = 0 and we have an error tolerance of ε (the absolute error in
calculating the root must be less that ε).
Bisection Algorithm:
Step 1: Find two numbers a and b at which f has different signs.
Step 2: Define c = a+b
2
.
Step 3: If b −c is less than or equal ε then accept c as the root and stop.
Step 4: If f (a)f (c) is less than or equal 0 then set c as the new b. Otherwise, set c as the
new a. Return to step 1.


Any kinds of equation you can run with this program.
For testing i am using some of equations like......

f(x ) = ($x*$x*$x)-(9*$x)+1;
f(x ) = (($x*$x)-(5*$x)+2);
f(x ) = (2*$x-3-cos($x));
f(x ) = (($x*$x*$x) - (21*$x)+3500);
f(x ) = ($x*$x-5*$x+2);
f(x ) = ($x*&log10($x))-1.2;
f(x ) = ($x*$x*$x)-(4*$x)-9;
f(x ) = $x*exp($x)-2;

If you face any problem.............
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Md. Alamgir Hossain
Dept. of Computer Science & Engineering
Jessore University of Science & Technology

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All source code........
https://alamgirhossainjust.blogspot.com/


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