On the efficient of adaptive methods to solve nonlinear equations

Torkashvand, Vali; Ezzati, Reza

doi:10.22075/ijnaa.2021.4799

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	On the efficient of adaptive methods to solve nonlinear equations
International Journal of Nonlinear Analysis and Applications
مقاله 24، دوره 12، شماره 1، مرداد 2021، صفحه 301-316 اصل مقاله (591.33 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.4799
نویسندگان
Vali Torkashvand^* ¹^{، 2}؛ Reza Ezzati³
¹‎‎‎Young Researchers and Elite Club, Shahr-e-Qods Branch, Islamic Azad University Tehran Iran
²Farhangian University, Tehran, Iran
³Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran
تاریخ دریافت: 27 اسفند 1397، تاریخ بازنگری: 24 دی 1398، تاریخ پذیرش: 03 بهمن 1399
چکیده
The main goal of this work, obtaining a family of Steffensen-type iterative methods adaptive with memory for solving nonlinear equations, which uses three self-accelerating parameters. For this aim, we present a new scheme to construct the self-accelerating parameters and obtain a family of Steffensen-type iterative methods with memory. The self-accelerating parameters have the properties of simple structure and easy calculation, which do not increase the computational cost of the iterative methods. The convergence order of the new iterative methods has increased from 4 to 8. Also, these methods possess very high computational efficiency. Another advantage of the new method is that they remove the severe condition $f'(x)$ in a neighborhood of the required root imposed on Newton's method. Numerical comparisons have made to show the performance of the proposed methods, as shown in the illustrative examples.‎
کلیدواژه‌ها
Nonlinear equations؛ Newton's interpolatory polynomial؛ Adaptive method with memory؛ The order of convergence؛ Self accelerating parameter‎‎

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On the efficient of adaptive methods to solve nonlinear equations