Higher Order Numerical Approaches for Nonlinear Equations by Decomposition Technique

Abstract

In this paper, a unique decomposition technique is implemented along with an auxiliary function for the best implementation. Some new and efficient techniques are introduced and analyzed for nonlinear equations. These techniques are higher ordered in approaching to the root of nonlinear equations. Some existing classical methods such as the Newton method, Halley method, and Traub's approach and their various modified forms are the special cases of these newly purposed schemes. These new iterative schemes are a good addition in existing methods and are also a comprehensive and generalized form for finding the solution of nonlinear equations.