| Abstrakt: |
In this paper, we present an efficient iterative algorithm for finding the root of a nonlinear equation. We develop this approach by incorporating the weight function technique in the second step and applying Steffensen's method in the third step. The presented scheme has been shown to be optimal based on convergence analysis, with an order of convergence of eight. We evaluate the performance of our method across various application problems, including beam designing models, fractional conversion, ideal and non-ideal gas laws, Planck's constant, multifactor effects, blood rheology models, volume calculations in the van der Waals equation, and stirred tank reactors. It demonstrates exceptional performance when compared to other iterative approaches with similar convergence orders. Furthermore, we explore the dynamical and fractal behavior of the proposed method and existing methods by using several complex polynomials as test functions and analyzing the basins of attraction. [ABSTRACT FROM AUTHOR] |
