On Dynamics of Iterative Techniques for Nonlinear Equation with Applications in Engineering

Mudassir Shams, Nazir Ahmad Mir, Naila Rafiq, A. Othman Almatroud, Saima Akram
2020 Mathematical Problems in Engineering  
In this article, we construct an optimal family of iterative methods for finding the single root and then extend this family for determining all the distinct as well as multiple roots of single-variable nonlinear equations simultaneously. Convergence analysis is presented for both the cases to show that the optimal order of convergence is 4 in the case of single root finding methods and 6 for simultaneous determination of all distinct as well as multiple roots of a nonlinear equation. The
more » ... ational cost, basins of attraction, efficiency, log of residual, and numerical test examples show that the newly constructed methods are more efficient as compared to the existing methods in the literature.
doi:10.1155/2020/5853296 fatcat:2upbsbovurarbhdvtdexrmmrty