10/8/20101Bisection MethodMajor: All Engineering MajorsAuthors: Autar Kaw, Jai PaulTransforming Numerical Methods Education for STEM Undergraduates
3Basis of Bisection MethodTheoremxf(x) xux An equation f(x)=0, where f(x) is a real continuous function, has at least one root between xland xuif f(xl) f(xu) < 0.Figure 1At least one root exists between the two points if the function is real, continuous, and changes sign.
xf(x) xux 6Basis of Bisection MethodFigure 4 If the function changes sign between two points, more than one root for the equation may exist between the two points.( )xf( )0=xf
7Algorithm for Bisection Method
8Step 1Choose xand xuas two guesses for the root such that f(x) f(xu) < 0, or in other words, f(x) changes sign between xand xu. This was demonstrated in Figure 1.xf(x) xux Figure 1