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

Document Type : Research Article

Author

• M. Dehghani-Madiseh

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

10.22067/ijnao.2022.74632.1092

Abstract

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.

Keywords

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

20.1001.1.24236977.2023.13.1.6.7

Main Subjects

• Numerical Analysis

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