Abstract
Here, we suggest a high-order optimal variant/modification of Schröder’s method for obtaining the multiple zeros of nonlinear uni-variate functions. Based on quadratically convergent Schröder’s method, we derive the new family of fourth -order multi-point methods having optimal convergence order. Additionally, we discuss the theoretical convergence order and the properties of the new scheme. The main finding of the present work is that one can develop several new and some classical existing methods by adjusting one of the parameters. Numerical results are given to illustrate the execution of our multi-point methods. We observed that our schemes are equally competent to other existing methods.
Highlights
There are several issues from chemistry, physics, applied mathematics, scientific computing, economics and engineering that can be transformed to Θ( x ) = 0. (1)It is almost inaccessible to find the solution by an analytical approach
We worry about the iterative schemes to find the multiple solution rm with known multiplicity m > 1 of the uni-variate function in Equation (1)
We are keen to construct a new general class of Schröder’s method where there is no need for the weight function(s) to develop new methods having optimal fourth-order convergence
Summary
Ramandeep Behl 1, *, Arwa Jeza Alsolami 1 , Bruno Antonio Pansera 2 , Waleed M. Al-Hamdan 1 , Mehdi Salimi 2,3 and Massimiliano Ferrara 2,4. ICRIOS—The Invernizzi Centre for Research on Innovation, Organization, Strategy and Entrepreneurship, Department of Management and Technology, Bocconi University, Via Sarfatti, 25, 20136 Milano, Italy
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