On an Efficient Family with Memory with High Order of Convergence for Solving Nonlinear Equations
Subject Areas : International Journal of Industrial Mathematics
V. Torkashvand
1
,
M. Kazemi
2
1 - Young Researchers and Elite Club, Shahr-e-Qods Branch, Islamic Azad University, Tehran, Iran.
2 - Department of Mathematics, Ashtian Branch, Islamic Azad University, Ashtian, Iran.
Keywords: With memory methods, Nonlinear equations, Efficiency index, Acceleration of convergence,
Abstract :
The primary goal of this work is to introduce general family Steffensen-like methods with memory of the high efficiency indices.To achieve this target two parameters are introduced which are calculated with the help of Newton’s interpolatory polynomial.It is shown that the R-order convergence of the proposed methods has been increased from 2;4;8,and 2^n to 3.5,7,14;and 3.5*2^n-1,respectively without any extra evaluation.Computational results confirm the efficient and robust character of presented methods.