Application of New Literacy and Newton Rapshon Methods in Numerical Solving of Roots of Nonlinear Equations

Abstract

Abstract: Solving non-linear equations is crucial in various scientific and engineering fields, especially when analytical solutions are difficult or impossible to obtain. This research compares the Newton-Raphson Method with the New Iterative Method for solving non-linear equations through numerical simulations using MATLAB. The objective is to evaluate both methods based on solution accuracy, convergence speed, and computational efficiency. The study examines four types of non-linear equations: trigonometric, polynomial, exponential, and logarithmic. Both methods are implemented in MATLAB and assessed based on the number of iterations, error values, and the accuracy of the obtained roots. The results indicate that the New Iterative Method is more efficient for solving trigonometric equations, requiring fewer iterations while maintaining comparable accuracy. In contrast, the Newton-Raphson Method performs better on polynomial equations, yielding more accurate results. For exponential and logarithmic equations, neither method proves optimal, with unrealistic or divergent root results and high error values. This highlights that the effectiveness of each method strongly depends on the type of function and the initial guess used. This study emphasizes the importance of selecting appropriate numerical methods and contributes to the practical and academic application of numerical analysis techniques.