mws_gen_nle_ppt_bisection(1) - Bisection Method Major All Engineering Majors Authors Autar Kaw Jai Paul http\/ Transforming

mws_gen_nle_ppt_bisection(1) - Bisection Method Major All...

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10/8/2010 1 Bisection Method Major: All Engineering Majors Authors: Autar Kaw, Jai Paul Transforming Numerical Methods Education for STEM Undergraduates
Bisection Method
3 Basis of Bisection Method Theorem x f(x) x u x An equation f(x)=0, where f(x) is a real continuous function, has at least one root between x l and x u if f(x l ) f(x u ) < 0. Figure 1 At least one root exists between the two points if the function is real, continuous, and changes sign.
x f(x) x u x 6 Basis of Bisection Method Figure 4 If the function changes sign between two points, more than one root for the equation may exist between the two points. ( ) x f ( ) 0 = x f
7 Algorithm for Bisection Method
8 Step 1 Choose x and x u as two guesses for the root such that f(x ) f(x u ) < 0, or in other words, f(x) changes sign between x and x u . This was demonstrated in Figure 1. x f(x) x u x Figure 1