## 5 Methods for Predicting Pavement Temperature
### Numerical and Finite Elements  
The numerical and finite element methods, as presented in Table 1, were carried out in four stages. In the first stage, the governing equation was formulated to determine the heat conduction in a pavement layer system; this equation is usually a one-dimensional (1-D) or two-dimensional (2-D) heat transfer profile simplified by a partial differential equation (PDE). First, the governing equation to account for the heat conduction within a pavement must be set up, which is usually a one-dimensional (1D) or two-dimensional (2D) heat transfer model represented by a time-dependent partial differential equation (PDE) [51]. The finite element method (FEM) is an advanced numerical method used for a variety of engineering problems. In FEM, the PDE is first converted from a robust model to the weak one [65; 66]. In the second stage, the \"Dirichlet boundary\" or the transit surface temperature, must be established [67], alternatively, a mixed-type edge that links climate parameters with the temperature gradient within the asphalt pavements depth. However, this link is accomplished by analysing the energy balance at the pavement surface [48; 54]. In the third stage, the spatial domain needs to discretised using a numerical method, such as finite-difference method, finite-element method, which results in a large system of ordinary differential equations (ODEs) in time [67; 68], FEM [44; 69], and a finite volume method (FVM) [62; 65]. In the fourth stage, a suitable time integrator is desired to solve these ODEs. For instance, this time integrator can either be a linear multistep method or a Runge-Kutta method [62]. In numerical analysis, the complex heat transfer process is considered to ensure that the models can be used universally, and the prediction of pavement temperature can be made under different conditions. One of the advantages of the analytical method is its ability to give a quick solution that can be used in real-time [70]. Furthermore, the calculation of the precision and time of numerical models is strongly influenced by roads density and the number of elements in the model [71]. The disadvantage of numerical methods however, is usually that they are not user-friendly, as they require proficiency in designing the FEM and good judgment to ensure convergence of the solutions [72]. The pavement temperature obtained through analytical solutions is influenced by heat conduction and its initial boundary value problem (IBVP). The analytical models use pavement surface temperature as the initial boundary value [73]. However, by performing this simplification, the influence of climatic parameters on pavement temperatures, such as wind speed, solar radiation, and air temperature, cannot be taken into account [62; 74; 75]. It should be highlighted that numerical models differ from regression equations in that, by making suitable assumptions, they may be used to obtain strict solutions for pavement temperature [70]. When compared with the analytical models, the boundary conditions in numerical models are observed to be far more complicated. Among the most frequently used numerical methods are FDM, FEM, and FVM.