Numerical Simulation of Nonlinear Equations by Modified Secant Method

By : Inderjeet, Rashmi Bhardwaj

Page No: 100-117

Abstract
Nonlinear equations are solved in a wide range of domains, including applied mathematics, computer science, and engineering. Iterative solutions are the only way to solve non-trivial situations of these equations.Thus, the creation of an effective and efficient iterative technique is crucial and can have a good effect on the process of determining the numerical solution of numerous real-world issues. The goal of this study is to create a novel, and effective iterative approach to solving nonlinear equations. The recently designed iterative approach is based on the classical Secant method for resolving nonlinear equations, which are investigated in various scientific and engineering domains. The nonlinear equation root finding approach that has been developed has an order of convergence of 1.84 and requires three beginning points instead of just two. By the use of multiple benchmark problems with varying iterations, the newly created method's convergence was demonstrated and its performance was compared with the traditional Secant method. According to the results, the newly designed method outperformed the conventional Secant method in terms of iterations and order of convergence. This provides support for the recently discovered method's credibility and offers hope for future study that will further perfect it.

Authors :
Inderjeet and Rashmi Bhardwaj : University School of Basic and Applied Sciences, Guru Gobind Singh Indraprastha University, Dwarka, Delhi , India
 

DOI: https://doi.org/10.32381/IAPQRT.2025.49.01.6