Some Improvments of The Cordero-Torregrosa Method for The Solution of Nonlinear Equations

محورهای موضوعی : مجله بین المللی ریاضیات صنعتی

M. Mohamadizade ¹ , T. Lotfi ² , M. Amirfakhriyan ³

1 - Department of Applied Mathematics, Hamedan Branch, Islamic Azad University, Hamadan, Iran.
2 - Department of Applied Mathematics, Hamedan Branch, Islamic Azad University, Hamadan, Iran
3 - Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran.

تاریخ دریافت : 1398/11/04 تاریخ پذیرش : 1399/11/27 تاریخ انتشار : 1400/04/10

کلید واژه: Iterative methods, The method without and with memory, Efficiency index, adaptive method, Convergence ‎order, Nonlinear equation,

چکیده مقاله :

In this paper, two adaptive methods with memory are improved based on Cordero- Torregrosa method. The technique of adaptive method increases the efficiency index as high as possible. The new derivative free methods have possessed the convergence order 7.46315 and 7.99315, and they only use the information from the last two iterations. Finally, we provide convergence analysis and numerical examples to illustrate the proposed methods.

چکیده انگلیسی:

در این مقاله، دو روش تطبیقی با حافظه بر اساس روش کوردرو- تروخروزا بهبود یافته است. تکنیک روش تطبیقی شاخص کارایی را تا حد ممکن افزایش می‌دهد. روش­های جدید بدون مشتق ارائه شده دارای مرتبه همگرایی  7/99315  و 7/46315  هستند و از اطلاعات دو تکرار گذشته استفاده می کنند. در نهایت، تجزیه و تحلیل همگرایی و مثال­های عددی را ارائه می­دهیم تا کارایی و کاربرد روش­های پیشنهادی را نشان دهیم.

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