Newton's method's basin of attraction for sign-changing solutions of concave and convex nonlinearities

In this paper, we will illustrate and visualize the chaotic behavior for solving the sign-changing solutions of concave-convex nonlinearities. We propose contractor iteration algorithm and bifurcation method to improve the computation speed and avoid local convergence of Newton-Raphson method. By this method, sign-changing numerical solutions will be computed and visualized in various domains.