Is there any example of an equation(polynomial or transcendental) such that when we use bisection method for finding the root , the sequence of the approximation of the root diverges from the original root of the equation?
Any kind of help or approach is great.
As bisection is a bracketing method, its boundaries will converge to a point with a sign change in the function, i.e., there will be (non-)positive and (non-)negative values in any neighborhood. For a continuous function, this will be a root.
If there are multiple roots in a given interval, the method of course can diverge from the observed root, but will converge to another root.