Abstract: Because it is often difficult to analyze the integrability and stability of one-dimensional dynamical systems with multiple equilibriums or transcending functions,it is a very significant problem for simplifying such dynamical systems.According to seven different cases of the functions on the right hand of one-dimensional dynamical systems with two or three equilibriums,seven kinds of non-linearized approximate systems are present by using Lagrange and Hermite interpolation polynomials.Approximate solutions are given by integrating the non-linearized approximate systems.It is found that the stability of the equilibriums is preserved by the new approximate methods.Finally,one of the non-linearized approximation methods is applied to analyze a pricing model of commodity concretely,for which the stability of equilibriums and the explicit approximate expression of the dynamical price are obtained.