Find in Library

In this paper, we introduce a new family of efficient and optimal iterative methods for finding multiple roots of nonlinear equations with known multiplicity <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>m</mi> <mo>&#8805;</mo> <mn>1</mn> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>. 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.