Generalization of the Secant Method for Solving Nonlinear Equations.

Abstract

This manuscript discusses a method for determining nonlinear equations roots from function having ( 1)th k  derivative which are continuous on an open interval containing the roots. The method used in this manuscript is a generalization of the Secant method. This generalization is by substituting the linear interpolation equation in the iteration equation by Secant method for the ( 1)th k  derivative polynomial interpolation equations. Convergence analyzing of the approximation roots sequence resulting in a degree of convergence which is greater than that of the Secant method and relatively similar to that of the Newton-Raphson method.