Optimal Fourth- and Eighth-Order Iterative Solver and Their Basins of Attraction - Murthy, Siva; Sathiragavan, M.; Mannan, Devendran; Madhu, Kalyanasundaram (Communications in Mathematics and Applications, 2025)
We developed a new, fourth- and eighth-order optimal approach for solving nonlinear equations in this study. With three function evaluations, the new methods’ convergence order is four; with four function evaluations, it is eight. Furthermore, according to the Kung-Traub hypothesis, it is optimal. In comparison to the suggested approaches, numerical results are provided to verify the superior computing efficiency of the current robust methods. We examine a wide range of practical issues, including projectile velocity to verify the suitability and efficacy of our suggested approaches. Lastly, in order to illustrate their dynamic behaviour on the complex plane, the basins of attraction are also provided.
Keywords: Basins of attraction; Multi-point iterations; Optimal order; Non-linear equation