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

Subject Areas : International Journal of Industrial Mathematics

مریم محمدی زاده ¹ (Department of Applied Mathematics, Hamedan Branch, Islamic Azad University, Hamadan, Iran.)
طاهر لطفی ² (Department of Applied Mathematics, Hamedan Branch, Islamic Azad University, Hamadan, Iran)
مجید امیرفخریان ³ (Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran.)

Received: 2020-01-24 Accepted : 2021-02-15 Published : 2021-07-01

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

Abstract :

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.

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