Applications of an Efficient Iterative Scheme for Finding Zeros of Nonlinear Equations and Its Basins of Attraction - Kakarlapudi, Navya; Mylapalli, Mani Sandeep Kumar; Sri, Ramadevi; Marapaga, Soujanya (Communications in Mathematics and Applications, 2023)
The recent research focuses on building several iterative methods over existing or classical numerical methods, such as Newton’s Method (NM), to solve nonlinear equations to attain higher-order convergence with an improving efficiency index over the produced models. To solve nonlinear equations, a three-step iterative strategy is suggested in this study. Additionally, we used our method in real-time applications for the azeotropic point of a binary solution, beam designing models, chemical engineering, fractional conversion, parachutist’s problem, Planck’s constant, classical projectile problem, and vertical stress. The numerical results demonstrate our method’s superior efficiency to some other existing methods of the same order. To illustrate the dynamic behaviour of basins of attraction in the complex plane, we also studied them.
Keywords: Nonlinear equations; Iterative method; Functional evaluations; Efficiency index; Convergence order; Basins of attraction