Extended ball convergence of a seventh order derivative free method for solving system of equations with applications

For solving nonlinear models in Banach spaces, we establish extended ball convergence of a seventh order derivative free method. Standard Taylor series technique that needs derivatives up to the eighth order was utilized in its existing convergence theorem. As compared to the existing study, our convergence work requires only the first derivative. Moreover, formulas for calculating the convergence radius and error estimates are obtained along with the area of uniqueness for the solution. We have therefore been able to increase the applicability of this efficient algorithm. Also, a visual tool, that is attraction basin, is employed to display the domain of convergence of this algorithm for finding zeros of complex polynomials. This study is concluded with the validation of our convergence result on application problems.