A New Three-Step Optimal Without Memory Iterative Scheme for Solving Non-Linear Equations with Basins of Attraction

Document Type : Research Paper

Authors

School of Advanced Sciences and Languages, VIT Bhopal University, Kothri-Kalan, Sehore, 466114, MP, India.

Abstract

The primary focus of this study is to introduce a new three-step iterative method without memory for root-finding by merging two different existing techniques. Based on the computational cost, the proposed method acquires optimal eight-order convergence with four functional evaluations (three evaluations for the function and one computation of first derivative). Furthermore, the suggested scheme supports the Kung Traub’s Conjecture with efficiency index of 1.682. We also established the convergence criteria developed for the root-finding technique and demonstrate the fact that the suggested approach is eighth-order convergent. In order to demonstrate the efficacy as well as application of the constructed root-finding technique, we addressed a few practical engineering models and some non-linear functions. In contrast to several existing approaches, this particular method converges more quickly. Finally, several forms of complex functions are taken into consideration under basins of attraction in order to observe the overall fractal behavior of the proposed technique

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 17 September 2024

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History

  • Receive Date: 10 November 2023
  • Revise Date: 29 July 2024
  • Accept Date: 08 September 2024

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