A new class of optimal four-point methods with convergence order 16 for solving nonlinear equations
For researchers in numerical analysis, this is an incremental improvement over existing optimal methods by achieving a higher convergence order (16) while maintaining the same number of evaluations.
The paper proposes a new class of optimal iterative methods for solving nonlinear equations, achieving convergence order 16 with four function evaluations and one derivative evaluation per iteration, matching the Kung-Traub conjecture. Numerical tests show competitive accuracy and basins of attraction compared to existing methods.
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.