Some Cubically Convergent Methods for Non-Linear Equations Based On Modified Homotopy Perturbation Method

Abstract

The development of numerical techniques for solving nonlinear algebraic equations is a subject of considerable interest. In the presented paper numerical methods based on the homotopy perturbation method (HPM) are proposed for solving non-linear algebraic equation s. Some modified forms of Newton-Raphson’s method are obtained. These methods show third-order convergence. Also, these methods are applied to some test problems to assess the validity and accuracy of the methods.