Trisection and Pentasection Method: A Modification of the Bisection Method for Solving Non-linear Algebraic Equations

The bisection method is one of the most used methods of solving non-linear equations, it is based on existence of a solution (root) in a given interval on a real number line, the interval is divided into two equal parts, it can be obviously seen that the root will be contained by one of the intervals, the interval that contained the root is later divided into another two sub-intervals while the interval that does not contain the root is dropped and never used again. The processes continued until the desired stopping criteria is reached, the interval that contain the roots is reduced to set of points, the root and its neighborhood. The root and its neighborhood may approximately serve as the desired root. In this research a new method, a modification of bisection method namely the trisection method and pentasection method are introduced, this method will be tested using several selected functions, the obtained results are then analyzed based on the number of iterations, the CPU time. The result from this research showed that the higher the number of the divisions of the interval, the higher the CPU time, while the number of iterations that yielded the result (root) reduces drastically. Moreover, the trisection method works faster than the Pentasection method.