Abstract
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.
Highlights
Solution of nonlinear equations are an important area of research in numerical analysis
In this branch of mathematics “Numerical analysis” usually deal with the continuous problem which come through daily life
Before the use of numerical algorithms analog devices were been used extensively in the science and amongst all the scientific Rule was common to the engineers which develop by Gunter in 1620
Summary
Solution of nonlinear equations are an important area of research in numerical analysis In this branch of mathematics “Numerical analysis” usually deal with the continuous problem which come through daily life. The homotopy perturbation method is used to solve a problem in pure and applied mathematics in different fields of science. This method is quiet efficient and allow us for choosing the auxiliary parameter arbitrary. The working rule of numerical methods is to find the approximate solutions of any mathematical problems on a defined interval either in time or distance. Noor [16, 17, 18, 19, 20, 21] and Noor et al.[22] modified the homotopy perturbation technique to suggest a wide class of iterative methods for solving nonlinear equations and related optimization problems. Comparions withe other known methods shows that the new methods perform better than the previous known methods
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
