Adaptive Steffensen-like Methods with Memory for Solving Nonlinear Equations with the Highest Possible Efficiency Indices

Subject Areas : International Journal of Industrial Mathematics

M‎. ‎J‎. Lalehchini ¹ (Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran.)
T. Lotfi ² (Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran.)
K. Mahdiani ³ (Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran.)

Received: 2018-11-18 Accepted : 2019-04-09 Published : 2019-12-01

Keywords: Adaptive methods, Iterative methods, Nonlinear equations, Steffensen-like method, Methods with memory,

Abstract :

The primary goal of this work is to introduce two adaptive Steffensen-like methods with memory of the highest efficiency indices. In the existing methods, to improve the convergence order applied to memory concept, the focus has only been on the current and previous iteration. However, it is possible to improve the accelerators. Therefore, we achieve superior convergence orders and obtain as high efficiency indices as possible.