Fractal Dynamics System Of Secant Method

Newton method is a classic numerical method for solving nonlinear equations.On the basis of Newton method, Secant Method used the difference quotient instead of calculating the value of derivative. his thesis derives improvements of Newton method. Extend the definitions of single-point chord method and double-point chord method with descent factorλ.Julia sets and Mandelbrot sets on the complex plane are fractal images generated by a simple iteration. In this paper, definitions of the convergence domain of parameter and the convergence domain of initial value are given. then we draw the convergence domain of single-point chord method and single-point chord method of complex function in the case of cube root and four unit root. Then gives the promotd definition of Mandelbrot set with two paraments, and show the image.In the last , with the complex mapping by the iteration function of double-point chord method,we expand the definitions of Julia sets and Mandelbrot sets, and show the image of generalized Mandelbrot set and the interception of generalized Julia set with different parameters.