| Volume 14, Number 6, 2024, Pages - DOI：10.11948/JAAC-2024-0009 |
| Dynamical Analysis of Optimal Iterative Methods for Solving Nonlinear Equations with Applications |
| Shahid Abdullah,Neha Choubey,Suresh Dara |
| Keywords:Iterative Method, Non-Linear Equation, Linear Combination, Weight Function Approach, Basin of Attraction |
| Abstract: |
| In this study, we introduced a new family of two and three-step iterative methods for solving non-linear equations. The proposed methods supports the Kung and Traub conjecture and hence are optimal by utilizing three function evaluations for fourth-order method and four functional evaluations for eighth-order method per cycle. We used the linear combination technique to obtain fourth-order method by combining Xiaojan’s method and Yu and Xu’s method while to get eighth-order method we use weight function approach. The convergence criteria of the proposed schemes are thoroughly covered in the two primary theorems. By contrasting our proposed schemes with certain existing ones on a few nonlinear models and some test functions, substantial numerical investigations are conducted to show the excellent performance and effectiveness of our suggested scheme. . Finally, several forms of complex functions are taken into consideration under basins of attraction in order to observe the overall fractal behavior of the proposed technique and some existing methods. |
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