Comparison of numerical methods to estimate the roots of a nonlinear and differentiable functions

We propose a new numerical method to estimate the root of the equation f(x) = 0, where f(x) is nonlinear and differentiable function on closed interval [a, b]. The proposed method is a hybrid of the Newton and Bisection methods. We we will compare our method with Newton-Raphson method, Bisection method, Brent's method and Secant method. We will study the speed of convergence for our method and compare it with other well-known methods by considering different nonlinear and differentiable functions with simple and multiple roots. Finally, we will generate a numerical algorithm for our proposed method.