An Optimal Eighth-Order Family of Iterative Methods for Multiple Roots

Saima Akram, Fiza Zafar, Nusrat Yasmin
2019 Mathematics  
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 ≥ 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
more » ... his paper and illustrates that the suggested family is efficient among the domain of multiple root finding methods.
doi:10.3390/math7080672 fatcat:2mq5lt4kjra5zistpq3jxvmkvq