NEW NINTH– AND SEVENTH–ORDER METHODS FOR SOLVING NONLINEAR EQUATIONS

Abstract

In this paper, we suggest and analyze some new higher-order iterative methods free from second derivative and used for solving of nonlinear equations. These methods based on a Halley iterative method and the weight combination of mid-point with Simpson quadrature formulas and using predictor–corrector technique. The convergence analysis of our methods is discussed. It is established that the new methods have convergence order nine and seven. Numerical tests show that the new methods are comparable with the well known existing methods and gives better results.