151. An Optimal Eighth-Order Family of Iterative Methods for Multiple Roots
- Author
-
Fiza Zafar, Saima Akram, and Nusrat Yasmin
- Subjects
Weight function ,010304 chemical physics ,Iterative method ,General Mathematics ,multiple roots ,lcsh:Mathematics ,Multiplicity (mathematics) ,010103 numerical & computational mathematics ,lcsh:QA1-939 ,01 natural sciences ,Computer Science::Digital Libraries ,efficiency index ,Nonlinear system ,ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION ,0103 physical sciences ,Computer Science (miscellaneous) ,nonlinear equations ,Applied mathematics ,Computer Science::Programming Languages ,0101 mathematics ,optimal iterative methods ,Engineering (miscellaneous) ,Root-finding algorithm ,Mathematics - Abstract
In this paper, we introduce a new family of efficient and optimal iterative methods for finding multiple roots of nonlinear equations with known multiplicity ( m &ge, 1 ) . We use the weight function approach involving one and two parameters to develop the new family. A comprehensive convergence analysis is studied to demonstrate the optimal eighth-order convergence of the suggested scheme. Finally, numerical and dynamical tests are presented, which validates the theoretical results formulated in this paper and illustrates that the suggested family is efficient among the domain of multiple root finding methods.
- Published
- 2019