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implement bisection method in c,
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Report Name : Implement bisection method in c Subject Name : Numerical methods Lab Course Code : CS-
Name : Md. Alauddin Maisha Maimuna ID : 006- 37 - 11 Lecturer, CSE Dept. : CSE Southern University
Remarks
Computer Science & Engineering Spring 2020
Name of the Report : Implement bisection method in C
Objective :
Description of Bisection method:
The method is applicable for numerically solving the equation f ( x ) = 0 for the real variable x , where f is a continuous function defined on an interval [ a , b ] and where f ( a ) and f ( b ) have opposite signs. In this case a and b are said to bracket a root since, by the intermediate value therom the continuous function f must have at least one root in the interval ( a , b ).
At each step the method divides the interval in two by computing the midpoint c = ( a + b ) / 2 of the interval and the value of the function f ( c ) at that point. Unless c is itself a root (which is very unlikely, but possible) there are now only two possibilities: either f ( a ) and f ( c ) have opposite signs and bracket a root, or f ( c ) and f ( b ) have opposite signs and bracket a root. The method selects the subinterval that is guaranteed to be a bracket as the new interval to be used in the next step. In this way an interval that contains a zero of f is reduced in width by 50% at each step. The process is continued until the interval is sufficiently small.
Explicitly, if f ( a ) and f ( c ) have opposite signs, then the method sets c as the new value for b , and if f ( b ) and f ( c ) have opposite signs then the method sets c as the new a. (If f ( c )=0 then c may be taken as the solution and the process stops.) In both cases, the new f ( a ) and f ( b ) have opposite signs, so the method is applicable to this smaller interval.
Iteration tasks
Screenshots of code:
