An extension of high-order Kou's method for solving nonlinear systems and its stability analysis

In this paper, Kou's method is extended to solve nonlinear systems. The convergence order of the iterative method is proved. Using fractal theory, we study the theoretical operators related to the iterative method, and analyze the stability of the iterative method. Properties related to strange fixed points and critical points are explored. The fractal results indicate that the iterative method is most stable when the parameter $\gamma$ equals zero. The extended iterative method is applied to solve the Hammerstein equation and some nonlinear systems. The dynamic plane and numerical experiments show that the extended iterative method can solve the nonlinear system of equations with good convergence and stability.