A family of eight-order interval methods for computing rigorous bounds to the solution to nonlinear equations

Iranian Journal of Numerical Analysis and Optimization

مقاله 18، دوره 13، شماره 1 - شماره پیاپی 24، خرداد 2023، صفحه 102-120   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2022.74632.1092

نویسنده

M. Dehghani-Madiseh^*

Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Iran.

چکیده

One of the major problems in applied mathematics and engineering sciences is solving nonlinear equations. In this paper, a family of eight-order interval methods for computing rigorous bounds on the simple zeros of nonlinear equations is presented. We present the convergence and er-ror analysis of the introduced methods. Also, the introduced methods are compared with the well-known interval Newton method and interval Ostrowski-type methods. Finally, we propose a technique based on the combination of the newly introduced approach with the extended interval arithmetic to find all of the roots of a nonlinear equation that are located in an initial interval.

کلیدواژه‌ها

Interval arithmetic؛ Nonlinear equations؛ Rigorous bounds؛ Con-vergence analysis

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