Open AccessSome Approximate Schemes for Solving Nonlinear Equations
Author(s) -
Muqadssa Shahzadi
Publication year - 2022
Publication title -
earthline journal of mathematical sciences
Language(s) - English
Resource type - Journals
ISSN - 2581-8147
DOI - 10.34198/ejms.9122.7991
Subject(s) - nonlinear system , convergence (economics) , generalization , mathematics , iterative method , taylor series , local convergence , homotopy perturbation method , homotopy analysis method , series (stratigraphy) , perturbation (astronomy) , algorithm , computer science , mathematical optimization , homotopy , mathematical analysis , paleontology , physics , quantum mechanics , pure mathematics , economics , biology , economic growth
Some iterative algorithms for solving nonlinear equation $f(x) = 0$ are suggested and investigated using Taylor series and homotopy perturbation technique. These algorithms can be viewed as extensions and generalization of well known methods such as Householder and Halley methods with cubic convergence. Convergence of the proposed methods has been discussed and analyzed. Several numerical examples are given to illustrate the efficiency of the suggested algorithms for solving nonlinear equations. Comparison with other iterative schemes is carried out to show the validity and performance of these algorithms.