A new Iterative Newton Raphson technique for the numerical simulation of Nonlinear Equations

Abstract

Nonlinear equations arise in various fields of science and engineering, often requiring numerical approximation methods for their solution. This paper presents a comparative analysis of the modified Newton-Raphson technique with other iterative techniques for the numerical simulation of nonlinear equations. The study evaluates the convergence rate, computational efficiency, and accuracy of the modified Newton-Raphson method in comparison to the standard Newton-Raphson method, the secant method, and the fixed-point iteration method. The performance of these techniques is assessed using benchmark problems and real-life applications, including fluid dynamics, heat transfer, and structural mechanics. The numerical simulations are conducted using MATLAB, and the results are presented in tabular forms. The findings demonstrate that the modified Newton-Raphson technique exhibits faster convergence and higher accuracy compared to the other iterative methods for a wide range of nonlinear equations. The paper also discusses the limitations and potential improvements of the modified Newton-Raphson technique, as well as its applicability to complex real-world problems. The study concludes by highlighting the significance of efficient and accurate numerical simulation techniques for nonlinear equations in advancing scientific research and engineering design.