An Efficient and Straightforward Numerical Technique Coupled to Classical Newton’s Method for Enhancing the Accuracy of Approximate Solutions Associated with Scalar Nonlinear Equations

Abstract

This study concerns the development of a straightforward numerical technique associated with Classical Newton’s Method for providing a more accurate approximate solution of scalar nonlinear equations. The proposed procedure is based on some practical geometric rules and requires the knowledge of the local slope of the curve representing the considered nonlinear function. Therefore, this new technique uses, only as input data, the first-order derivative of the nonlinear equation in question. The relevance of this numerical procedure is tested, evaluated, and discussed through some examples.

A New Iterative Numerical Continuation Technique for Approximating the Solutions of Scalar Nonlinear Equations

“…Although, in the literature, the most used numerical methods are either the classical Newton's technique [3,4,6] or modified Newton-type procedures [7][8][9][10], they suffer from the main disadvantage of being held in check in the presence of critical points [11]. In order to overcome this deficiency, we propose to develop a new iterative algorithm applied to a numerical continuation procedure [5] for providing the approximate solutions associated with parameterized scalar nonlinear equations.…”