A three-free-parameter class of power series based iterative method for approximation of nonlinear equations solution

Iranian Journal of Numerical Analysis and Optimization

مقاله 21، دوره 13، شماره 2 - شماره پیاپی 25، شهریور 2023، صفحه 157-169   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2022.74901.1095

نویسندگان

O. Ogbereyivwe^{* 1}؛ O. Izevbizua²

¹Department of Mathematics and Statistics, Delta State University of Science and Technology, Delta State, Nigeria.

²Department of Mathematics, University of Benin, Benin City, Nigeria.

چکیده

In this manuscript, for approximation of solutions to equations that are nonlinear, a new class of two-point iterative structure that is based on a weight function involving two converging power series, is developed. For any method constructed from the developed class of methods, it requires three separate functions evaluation in a complete iteration cycle that is of order four convergence. Also, some well-known existing methods are typical members of the new class of methods. The numerical test on some concrete methods derived from the class of methods indicates that they are effective and competitive when employed in solving a nonlinear equation.

کلیدواژه‌ها

Newton method؛ Iterative method؛ Power series؛ Weight function

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