## 5 Discussion  
To investigate the proposed method, five numerical examples are conducted. Based on the results, the discussions are carried out as follows.  
We conduct the sensitivity analysis and results compared with the analytical solution in example 1 and example 2. Results obtained demonstrate that the MAE is in the order of \(10^{-16}\). It is obvious that the SCA may yield highly accurate results. To further illustrate the advantages of the proposed approach, examples 3 and 4 are conducted to investigate the accuracy of temporal discretization. From the results of this study, we indicate that the MAE of the SCA remains in the order of \(10^{-5}\) to \(10^{-9}\). We also compare the MAE of our method and those of the FDM. The MAE of the FDM is only on the order of \(10^{-2}\) and \(10^{-3}\). It is significant that the proposed method may have more accurate numerical results than those of the conventional time-marching FDM.  
We propose the spacetime collocation approach for solving the tide-induced groundwater response. For the solving of the tide-induced groundwater response in a coastal confined aquifer with an estuary tidal-loading boundary using the proposed method, the boundary points are placed in the spacetime region. Hence, both initial as well as boundary values are considered as boundary conditions on the spacetime boundaries. The one-dimensional initial value problem can then be regarded as a two-dimensional inverse BVP. Accordingly, the transient problems for tide-induced head response in a coastal confined aquifer may be solved without utilizing the time-stepping techniques. Besides, more accurate numerical results for solving transient problems can be obtained.  
However, the SCA has to derive the general solutions as the basis functions for the governing equation of one-dimensional tide-induced groundwater response in a coastal confined aquifer utilizing the separation of variables. The solutions of the tide-induced head response are then described as a series adopting the addition theorem. As a result, the proposed technique can only deal with the linear governing equation.  
Furthermore, another disadvantage is that the transformation of the original one-dimensional problem into two-dimensional spacetime boundary value problem may increase the volume of computing. Because the proposed technique is a boundary-type method, the points may be collocated only on the spacetime boundary of the domain. Since we do not need to place any collocation points inside the domain, the proposed method may be more efficient than other numerical approaches. Although the array of the computation from two-dimensional spacetime boundary value problem may be larger than the original one-dimensional problem, it is found that the benefits of the compromise for increasing the volume of the computation to obtain highly accurate results for tide-induced groundwater flow problem may be acceptable.  
Figure 18: Comparison of the computed groundwater response with measured data.  
In addition, similar to other boundary-type meshless methods, the proposed method may also suffer from the numerical instability due to the ill-posed phenomenon of the meshless method for solving two- or three-dimensional problems.