Three‑point iterative algorithm in the absence of the derivative for solving nonlinear equations and their basins of attraction | ||
| Journal of the Egyptian Mathematical Society | ||
| Volume 29, Issue 1, 2021, Pages 1-17 PDF (3.01 M) | ||
| Document Type: Original Article | ||
| DOI: 10.1186/s42787-021-00132-9 | ||
| Author | ||
| Mohamed S. M. Bahgat* | ||
| Mathematics Department, Faculty of Science, Minia University, Minia, Egypt. | ||
| Abstract | ||
| In this paper, we suggested and analyzed a new higher-order iterative algorithm for solving nonlinear equation g(x) = 0, g : R −→ R, which is free from derivative by using the approximate version of the frst derivative, and we studied the basins of attraction for the proposed iterative algorithm to fnd complex roots of complex functions g : C −→ C. To show the efectiveness of the proposed algorithm for the real and the complex domains, the numerical results for the considered examples are given and graphically clarifed. The basins of attraction of the existing methods and our algorithm are ofered and compared to clarify their performance. The proposed algorithm satisfed the condition such that |xm − α| < 1.0 × 10−15, as well as the maximum number of iterations is less than or equal to 3, so the proposed algorithm can be applied to efciently solve numerous type non-linear equations. | ||
| Keywords | ||
| : Nonlinear equations; Free derivative; Order of convergence; Fractal; Basin of attraction | ||
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