A new iterative with memory class for solving nonlinear ‎equations‎

Subject Areas : International Journal of Industrial Mathematics

P. ‎Bassiri‎ ¹ , P. Bakhtiari‎‎ ² , S. Abbasbandy‎ ³

1 - Department of Mathematics, Payame Noor University (PNU), P. O. Box, 19395-3697, Tehran, Iran.
2 - Young Researchers and Elite Club, Hamedan Branch, Islamic Azad University, Hamedan, Iran.
3 - Department of Mathematics, Imam Khomeini International University, Ghazvin, 34149-16818, Iran.

Received: 2016-08-22 Accepted : 2016-08-22 Published : 2016-08-01

Keywords: Multi-step methods, Nonlinear equations, Optimal order, Methods with memory, Kung-Traub's ‎conjecture.‎,

Abstract :

In this work we develop a new optimal without memory class for approximating a simple root of a nonlinear equation. This class includes three parameters. Therefore, we try to derive some with memory methods so that the convergence order increases as high as possible. Some numerical examples are also ‎presented.‎‎