A New Third-Order Family of Multiple Root-Findings Based on Exponential Fitted Curve

In this paper, we present a new third-order family of iterative methods in order to compute the multiple roots nonlinear equations when multiplicity (m?1) is known advance. There plethora point-to-point methods, available literature; but our are based on geometric derivation and converge required zero even though derivative becomes or close vicinity zero. We use exponential fitted curve tangency conditions for development schemes. Well-known Chebyshev, Halley, super-Halley Chebyshev–Halley special members schemes m=1. Complex dynamics techniques allows us see relation between element wideness basins attraction simple roots, quadratic polynomials. Several applied problems considered demonstrate performance comparison with existing ones. Based numerical outcomes, deduce that illustrate better over earlier case high multiplicity.