This paper presents a full numerical model accounting for the heat transfer and phase-change by combining the modified Keller-Miksis equation with the second order term of compressibility of liquid, partial differential equations (PDEs), and Hertz-Knudsen-Langmuir equation. Then, a simplified model for studying the dynamics of the cavitation bubble or bubble excited by the acoustic waves is proposed. The major contribution is to simplify the full model with PDEs to a set of coupled ordinary differential equations (ODEs). Specifically, two energy PDEs are converted to three ODEs by coupling the boundary conditions. The comparison among the full model and other simplified models is used to validate the accuracy and superiority of the simplified model, from which the application range of the proposed simplified model can be determined.