Dynamical behavior analysis of an eighth-order Sharma's method

We analyze the dynamical behavior of an eighth-order Sharma's iterative scheme, which contains a single parameter, with respect to an arbitrary quadratic polynomial using complex analysis. The eighth-order Sharma's iterative scheme is analytically conjugated to a rational operator on the Riemann sphere. We discuss the strange fixed points of the rational operator and present its stable region graph. Additionally, we briefly investigate the superattracting point and the critical point, which have an impact on the Sharma's iterative scheme discussed. Finally, we present the dynamical planes for different parameter values using the complex dynamics tool, which helps us select more effective members of the Sharma's iterative scheme. Numerical experiments are conducted to verify the theoretical results.