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

摘要

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.