COMMAX 2020 UiTM Kampus Kuala Terengganu

In this project, the methods that are chosen are Bisection method, Newton’s method, Modified Newton’s method and Hybrid method. A new algorithm of Hybrid method which is the combination of Bisection method and Modified Newton’s method will be designed and implemented. In this project, the new hybrid method will be compared with Bisection method, Newton’s method and Modified Newton’s method. These methods are difference between the algorithms of itself. For the Bisection method, the interval is divided into two equal intervals while for Newton’s method and Modified Newton’s method, it uses an initial guess point as its input. Newton’s method will be modified to get the roots because it more accurate and efficient rather than Newton’s method. Meanwhile, hybrid method takes a first approximation by apply two times Bisection method and complete the correct approximation by using the Modified Newton’s method. The root of the nonlinear equation is identified either in the first or second interval by determining the sign of the product of the function at the both interval ends. The iterative sequence is continued until stop criterion has been reached. For this research, a Bisection – Modified Newton’s hybrid method is introduced. All methods are tested for several selected functions such as trigonometric, exponential, logarithmic and cubic polynomial function by using Maple software. The results are then analyses to determine the accuracy and efficiency if this new method especially the Modified Newton’s method and new Hybrid method based on the number of iterations and CPU times.