A new class of optimal four-point methods with convergence order 16 for solving nonlinear equations

作者：Sharifi Somayeh; Salimi Mehdi^*; Siegmund Stefan; Lotfi Taher

来源：Mathematics and Computers in Simulation, 2016, 119: 69-90.

DOI：10.1016/j.matcom.2015.08.011

• Simple root
• Four-step iterative method
• Kung and Traub conjecture
• Optimal order of convergence
• Computational efficiency

We introduce a new class of optimal iterative methods without memory for approximating a simple root of a given nonlinear equation. The proposed class uses four function evaluations and one first derivative evaluation per iteration and it is therefore optimal in the sense of Kung and Traub's conjecture. We present the construction, convergence analysis and numerical implementations, as well as comparisons of accuracy and basins of attraction between our method and existing optimal methods for several test problems.

• 出版日期2016-1