5. DISCUSSION
To investigate the proposed method, five numerical examples are conducted. Based on the results, the discussions are carried out as follows.
  1. We conduct the sensitivity analysis and results comparison with the analytical solution in example 1 and example 2. Results obtained demonstrate that the MAE can reach to the order of 10-16. It is significant that the SCA may obtain highly accurate results. The accuracy of the proposed method is close to that of the analytical method. To further demonstrate the advantages of the proposed method, example 3 and 4 are conducted to investigate the accuracy of temporal discretization. From 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.
  2. In this article, 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 the boundary and initial values are considered as boundary conditions on the boundary of the spacetime. The one–dimensional initial value problem can then be regarded as a two–dimensional inverse BVP. Accordingly, the transient problems for tide–induced groundwater 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 using the proposed method. However, 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.