An improved Newton-Raphson method with quadratic convergence for solving nonlinear transcendental equations

Abstract

This paper presents a new scheme to find a non-zero positive root of the non-linear single variable equations. The proposed method is based on the grouping of the arc sine series and Newton-Raphson method. The proposed method is implemented in MATLAB and is applied to various models of problems to ensure the methods applicability. The proposed method is studied on number of numerical examples and results signify that our method is better and more effective as comparable to renowned methods. These results are depicted through error analysis. The convergence of proposed method is proven to be quadratically convergence.