A derivative free globally convergent method and its deformations

The motive of the present work is to introduce and investigate the quadratically convergent Newton’s like method for solving the non-linear equations. We have studied some new properties of a Newton’s like method with examples and obtained a derivative-free globally convergent Newton’s like method using forward difference operator and bisection method. Finally, we have used various numerical test functions along with their fractal patterns to show the utility of the proposed method. These patterns support the numerical results and explain the compactness regarding the convergence, divergence and stability of the methods to different roots.