The development of Newton’s method by enhancing the starting point

In general, nonlinear problems cannot be solved analytically. A special theory or method is needed to simplify calculations. Many that are too complex, an exact solution support numerical solution. There many methods can used solve problems, including the Bisection, Secant and Newton methods, also known as Newton-Raphson method. However, these for large-scale of programming problems; example which does not always converge if it takes wrong initial value. The widely find approximations roots real functions. Therefore, necessary develop without using other in order have a higher convergence. This research literature study compiled based on references with step understanding appear from use Newton's method, base problem divergence oscillation. Newtonian was developed modification but took two starting points. Then prove super-quadratic convergence proposed by extending Taylor expansion giving assuming error rate. After that, stability test model carried out provides application solving root search seen comparison.