Solving for Roots of Nonlinear Equations by Taylor Expansion
Keywords:Nonlinear equation, Taylor expansion, Newton-Raphson Method
AbstractThis paper illustrates an iterative numerical method to find roots of nonlinear equation in a form of f(x)=0Â by using 2nd and 3rd order Taylor expansion. The numerical results show that this iteration method is faster than Newtonâ€“Raphson, hybrid iteration and the new hybrid iteration method. Also this iteration method needs less than number of functional evaluations than the others.
Nasr Al-Din Ide, â€œA new Hybrid iteration method for solving algebraic equationsâ€, Applied Mathematics and Computation, vol. 195, pp. 772-774, 2008.
Amit kumar Maheshwari, â€œA fourth order iterative method for solving nonlinear equationsâ€, Applied Mathematics and Computation, vol. 211, pp. 383-391, 2009.
Avram Sidi, â€œUnified treatment of Regular Falai, Newtonâ€“Raphson, Secent, and Steffensen methods for nonlinear equationsâ€, Journal of Online Mathematics and Its Applications, pp.1-13, 2006.
How to Cite
- Papers must be submitted on the understanding that they have not been published elsewhere (except in the form of an abstract or as part of a published lecture, review, or thesis) and are not currently under consideration by another journal published by any other publisher.
- It is also the authors responsibility to ensure that the articles emanating from a particular source are submitted with the necessary approval.
- The authors warrant that the paper is original and that he/she is the author of the paper, except for material that is clearly identified as to its original source, with permission notices from the copyright owners where required.
- The authors ensure that all the references carefully and they are accurate in the text as well as in the list of references (and vice versa).
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Attribution-NonCommercial 4.0 International that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
- The journal/publisher is not responsible for subsequent uses of the work. It is the author's responsibility to bring an infringement action if so desired by the author.