On 4th Order Iterative Methods for Nonlinear Equations

Abstract

The main objective of this study is Fourth-order iterative techniques to solve nonlinear equations. In numerous scientific and engineering problems, the nonlinear equations are indispensable and their solution are based on suitable and accurate methods. Fourth-order iterative techniques have been used to solve equations due to their high computational and ideal convergence order. The fourth-order iterative techniques of Chun, Ren, et al., and Qureshi et al. are reviewed and analyzed with a focus on function per iteration, error term, and efficiency indices in this study. Using a comparative analysis, we have demonstrated a new technique from Noor which is computationally efficient and accurate. The results also show that better error correction and optimization techniques significantly contribute to the performance of these methods. In order of convergence and efficiency comparison of their performance, this work provides important understanding.