Abstract: The most common method for numerical solving is New ton iteration method. Generally, the method can reach the solution quickly. It needs a well-designed initial value and is quite sensitive to the initial value. When the initial value changed slightly, the method may emanate or converge the process and generate an unexpected solution. The random selection of the initial value in the initial design stage often makes the initial condition not good enough and gives Newton Raphson method difficulties to converge. We've revealed two major defects after analysis on the traditional numerical method in the application of the nonlinear equation solution:(1) It is too relied on the initial point; (2) The convergence results lack of consistency. In this paper the ergodicity of chaos algorithm introduced can help resolve the issues mentioned above.