On new sixth and seventh order iterative methods for solving non-linear equations using homotopy perturbation technique

Srinivasarao Thota; P Shanmugasundaram

doi:10.1186/s13104-022-06154-5

On new sixth and seventh order iterative methods for solving non-linear equations using homotopy perturbation technique

BMC Res Notes. 2022 Jul 30;15(1):267. doi: 10.1186/s13104-022-06154-5.

Authors

Srinivasarao Thota¹, P Shanmugasundaram²

Affiliations

¹ Department of Mathematics, School of Sciences, SR University, Warangal, Telangana, 506371, India. srinithota@ymail.com.
² Department of Mathematics, College of Natural & Computational sciences, Mizan Tepi University, Mizan Teferi, Ethiopia.

Abstract

Objectives: This paper proposes three iterative methods of order three, six and seven respectively for solving non-linear equations using the modified homotopy perturbation technique coupled with system of equations. This paper also discusses the analysis of convergence of the proposed iterative methods.

Results: Several numerical examples are presented to illustrate and validation of the proposed methods. Implementation of the proposed methods in Maple is discussed with sample computations.

Keywords: Homotopy perturbation technique; Iterative methods; Nonlinear equations; Order of convergence.