Second generation wavelet based on adaptive solution of wave equation

A second generation wavelet is developed for the adaptive numerical solutions of wave equations. The second-order temporal derivative of wave equation is reduced to first-order one by using a Hamilton approach. Second generation wavelet decomposition is used for the construction of dynamically adaptive computing grid, while a special finite difference scheme is introduced for the calculation of spatial derivative. By using a semi-group method, the discretized solution in time can be represented in an explicit recursive form. Numerical examples show the effectiveness of this method.