Optimal parametric families of derivative free iterative structures for locating nonlinear equation solution

Theory of Approximation and Applications

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 02 آبان 1402

نوع مقاله: Research Articles

نویسندگان

Oghovese Ogbereyivwe^{* 1}؛ Salisu Shehu Umar²

¹Dept. of Mathematics, Faculty of Sciences, Delta State University of Science and Tech., Ozoro, Nigeria

²Auchi Polytechnic, Auchi, Nigeria.

چکیده

One golden rule in the development of new iterative structure for locating the solution of nonlinear equation is that, it should be
of low computation cost. The presence of functions derivatives evaluations in an iterative structure no doubt, increases its implementation
cost. More so, obtaining derivative of some complex functions can be big
challenge. In this regard, three class of fourth, seventh and eight-order
derivative free iterative structures are developed and put forward in
this manuscript.The convergence test on the developed iterative structures were established using some designed computer programs that are
executed in MATHEMATICA software environment. Some nonlinear
problems were solved using the developed iterative structures and results obtained were placed in juxtaposition with that of some existing
contemporary methods.

کلیدواژه‌ها

Nonlinear equation؛ Iterative structure؛ Steffenson method؛ optimal order of convergence