Some Higher Order Newton-Like Methods for Solving System of Nonlinear Equations and Its Applications

Abstract

In this paper, we have proposed three higher order iterative methods of convergence order four, five and six for solving system of nonlinear equations. New weight functions are included in the second term of the Newton’s method in order to get higher order methods. Also, we achieve higher order accuracy with only one inverse of Jacobian matrix. In fact, a special attention has been given to use less number of linear system in the iterative process. Fourth order method is a two step method whereas new fifth and sixth order methods are composed of three steps, namely, Newton iteration as the first step and weighted Newton iteration as the second and third step. It is proved that the root \(\alpha \) is a point of attraction for the new iterative schemes. The performance of the new methods is verified through numerical examples. As an application, we have implemented the present methods on Chandrasekhar’s equation and 1-D Bratu problem.