The n-th section method: A modification of Bisection

Abstract

Bisection method is the easiest method to find the root of a function. This method is based on the existence of a root on a specified interval. This interval is then halved or divided into two parts. The root is known to be laying in either one of these interval. The iterative sequence is continued until a desired stopping criterion is reached. In this research, a new modification of bisection method namely fourth section and sixth section methods are introduced. These methods are tested for several selected functions by using Maple software. The results are then analyzed based on the number of iterations and the CPU times. Based on the results, it is shown that when the interval increases, the CPU will also increase. However, the number of iterations is reduced significantly.