On method of osculating circle for solving nonlinear equations

In this paper we present a new algorithm for solving nonlinear equations and this method requires the use of the first and second derivatives of the function as Halley's, Laguerre's, Chebyshev's and other classical methods do. It has well known geometric interpretation and admits its geometric derivation from a circle. Further, the executed comparative numerical experiments show that this new method competes well with the known classical methods and has cubic convergence.