Comparative Study of Nonlinear Root Finding Using Improvised Secant Methods

The nonlinear transcendental or algebraic equation problem is one of the important research areas in numerical analysis, and the iterative methods are playing an important role to find approximate solutions. The Secant method is one of the best iterative methods since it only requires a single evaluation of function. However, the Secant method has low convergence order, thus many improvised Secant methods have been developed by other researchers. Even though improvise secant method has been developed vastly, comparative study of these methods is relatively scarce, and the novelty of this paper is to assess critical numerical performances of the methods. Therefore, in this study, two algorithms based on the Secant method which are the exponential method, and three-point Secant method were used to compare with the Secant method to evaluate the roots for nonlinear equations. The three methods were tested using different initial values in various transcendental functions such as polynomial, exponential, logarithm, trigonometric and some combinations of linear, exponential, polynomial, and trigonometric functions to determine the best method among three methods and to determine the behavior of these method. All the computation results were developed using Graphical User Interface (GUI) in MATLAB environment to get the results and as the visual indicator representations. The obtained results show that the threepoint Secant method has the least number of iterations than the Secant method and exponential method in six numerical results. Conclusively, the three-point Secant method is the best iterative method since the method converged to the roots faster than other two.