Basins of Attraction of an Iterative Scheme and Their Applications - Marapaga, Soujanya; Mylapalli, Mani Sandeep Kumar; Kakarlapudi, Navya; Boddana, Simhachalam; Chaganti, Pragathi (Communications in Mathematics and Applications, 2023)
This work presents a seventh-order iterative scheme with the help of a variational iteration technique for finding the root of the nonlinear equations. The convergence analysis of the method is discussed and shows that it has seventh-order convergence with four functional evaluations per iteration. Therefore, the efficiency index is 1.6265. The computational performance of the suggested scheme is compared with some well-existing methods of the same order and is tested on various nonlinear equations, including real-world problems. Furthermore, we analyzed the dynamics of the proposed method using basins of attraction in the complex domain by taking some polynomial functions and compared our results with other known methods.
Keywords: Nonlinear equations; Iterative method; Efficiency index; Convergence order; Basins of attraction