Lab for the Bisection Method

Bisection Method. To find a root of the equation f(x) = 0 in the interval [a,b]. Proceed with the method only if f(x) is continuous and f(a) and f(b) have opposite signs.

Example. Find the solution to the equation in the interval [0,3].
Use the bisection method to compute a solution with an accuracy of .
Solution. Since we will use 21 iterations.

Bisection[0.0, 3.0, 21]

 
 

Report to be handed in.

Computer Exercises

Exercise 1. Find solutions to the equation on the intervals [0,1], [1.5, 2.5] and [3,4]. Use the bisection method to compute a solution with an accuracy of . Determine the number of iterations to use. Include a printout of iterations in your report.
Solution. Since you should use 23 iterations.

Bisection[0.0, 1.0, 23];

Exercise 2. Consider f(x) = tan(x) on the interval (0,3). Use the 20 iterations of the bisection method and see what happens. Explain the results that you obtained.

f[x_] = Tan[x]



 
 
Bisection[0.0, 3.0, 20];

The function 0 = tan(x) does not have a solution in the interval (0,3). However, it does have a vertical asymptote at x=. Since tan(x) has opposite signs on each side of x=, the bisection method converges to .

(c) John H. Mathews, 1998