Some Multiple and Simple Real Root Finding Methods

Abstract

Solving nonlinear equations with root finding is very common in science and engineering models. In particular, one applies it in mathematics, physics, electrical engineering and mechanical engineering. It is a researchable area in numerical analysis. This present work focuses on some iterative methods of higher order for multiple roots. New and existing novel multiple and simple root finding techniques are discussed. Methods independent of a multiplicity m of a root r, which function very well for both simple and multiple roots, are also presented. Error-correction and variatonal technique with some function estimations are used for the constructions. For the analysis of orders of convergence, some basic theorems are applied. Ample test examples are provided (in C++) for test of efficiencies with suitable initial guesses. And convergence of some methods to a root is shown graphically using matlab applications.

Keywords:Iterative algorithms, error-correction, variational methods, multiple roots, applications