COMMAX 2020 UiTM Kampus Kuala Terengganu

Numerical root-finding methods are important problem for nonlinear equations and have a wide variety of applications in science and engineering. Numerical techniques are explored when an analytic solution are unclear. Some root problems can present difficulties for algorithms which often perform well. There is not a single algorithm that works best for each function. Therefore, the idea of root-finding methods based on the Hybrid method. In this project, a new algorithm which is a hybrid method between the Modified Bisection method and Newton’s method will be designed and implemented. The result confirms that the new algorithm outperforms Modified Bisection method, Newton’s method and Secant method with respect to computational iterations. All method chosen are used in numerical analysis to find the actual root of a single nonlinear equations. The new method is guaranteed requires less computational iterations. But this new method is not the best method among others three chosen method which is Modified Bisection method, Newton’s method and Secant method. Modified bisection method is for continuous functions. So the interval is divided into two equal intervals and also uses the mid-point as the approximate value. While the Newton’s method is for differentiable function and an initial guessing point used as input. Meanwhile, hybrid method takes a first approximation by apply the Bisection method, followed by the Modified Bisection method and complements by Newton’s method. The iterative repeated until the desired stop criteria has been met. These methods are tested using Maple software. The results are then analyzed to determine the accuracy and efficiency of this new method based on the number of iterations and the CPU times. Based on the results, it is shown that the new iterative method can decrease the number of iterations and CPU iv times that is applied in this project. This can be attributed to the iterative methods that converge more rapidly than others chosen method.