Title of article :
Adaptive Steffensen-like Methods with Memory for Solving Nonlinear Equations with the Highest Possible Efficiency Indices
Author/Authors :
Lalehchini, M. J Department of Applied Mathematics - Hamedan Branch - Islamic Azad University , Lotfi, T Department of Applied Mathematics - Hamedan Branch - Islamic Azad University , Mahdiani, K Department of Applied Mathematics - Hamedan Branch - Islamic Azad University
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, considering the time from the first to the current iterations. Therefore, we achieve superior convergence orders and obtain as high efficiency indices as possible . These are the main contributions of this work.
Keywords :
Nonlinear equations , Iterative methods , Steffensen-like method , Methods with memory , Adaptive methods , R-order
Journal title :
Astroparticle Physics
