Treatment of Boundary Conditions in the Application of Wavelet-Galerkin Method to an SH Wave Problem

One of main problems with the Wavelet-Galerkin is the treatment of boundary conditions. It is sloved by our method which is referred to as Fictitious Boundary Approach. In this approach, a fictitious boundary is assumed to tackle the difficulty of treating boundary conditions. And an additional condition is also made in order to ensure the real solution. This method is adapted to all the three kinds of boundary conditions in the theory of differential equation. To support our method, an SH wave mode problem in a plate is solved, and its numeral result is compared with the exact solution. Although the Wavelet-Galerkin has very good features for solving differential equations, we find that it is still difficult to represent the infinite resonance solution after investigating the error convergence near the resonance point. And we emphasize the importance of selecting a proper scale j especially to represent the solution near the resonance.