Extended Seventh Order Derivative Free Family of Methods for Solving Nonlinear Equations

A plethora of applications from Computational Sciences can be identified for a system nonlinear equations in an abstract space. These are mostly solved with iterative method because analytical does not exist such problems. The convergence the is established by sufficient conditions. Recently, there has been surge development high order methods. Local results reveal degree difficulty when choosing initial points. However, these methods may converge even cases guaranteed Moreover, it known advance how many iterations should carried out to reach certain error tolerance. Furthermore, no computable information provided about isolation solution region containing it. aforementioned concerns constitute motivation writing this article. novelty works expansion applicability under ω−continuity conditions considered involved operator. technique demonstrated using derivative-free seventh three-step method. was found that used same effectiveness as other inverses linear operators. also uses operators appearing This contrast earlier utilizing derivatives or divided differences on which problem at hand. numerical experiments complement theory.