Optimal Newton-Secant like methods without memory for solving nonlinear equations with its dynamics
For researchers in numerical analysis, this work provides computationally efficient iterative methods for solving nonlinear equations, though it is an incremental improvement over existing optimal methods.
The paper develops two optimal Newton-Secant like methods for solving nonlinear equations, achieving convergence orders four and eight with only three and four function evaluations per iteration, respectively, thereby supporting the Kung-Traub conjecture. Numerical experiments and basin of attraction analysis demonstrate their efficiency compared to existing methods.
We construct two optimal Newton-Secant like iterative methods for solving non-linear equations. The proposed classes have convergence order four and eight and cost only three and four function evaluations per iteration, respectively. These methods support the Kung and Traub conjecture and possess a high computational efficiency. The new methods are illustrated by numerical experiments and a comparison with some existing optimal methods. We conclude with an investigation of the basins of attraction of the solutions in the complex plane.