Optimal Fourth-Order Weerakoon–Fernando-Type Methods for Multiple Roots and Their Dynamics
In this paper, we present optimal fourth-order methods for finding multiple roots of non-linear equations, where the multiplicity is known in advance. These methods are based on the third-order method given by Weerakoon and Fernando for simple roots. The dynamical behavior of these methods around multiple roots is studied using basin of attraction in complex plane. We also present numerical examples to confirm our theoretical results.
KeywordsNon-linear equations Newton-type method multiple root complex dynamics fixed and critical points basin of attraction
Mathematics Subject Classification65H05
- 9.Petkovic, M.S., Neta, B., Petcovic, L.D., Dzflnic, J.: Multipoint Methods for Solving Nonlinear Equations. Elsevier, Waltham, MA (2013)Google Scholar