Solving hyperbolic PDEs using interpolating wavelets

A method is presented for adaptively solving hyperbolic PDEs. The method is based on an interpolating wavelet transform using polynomial interpolation on dyadic grids. The adaptability is performed automatically by thresholdi ng the wavelet coefficients. Operations such as differentiation and multipl ication are fast and simple due to the one-to-one correspondence between po int values and wavelet coefficients in the interpolating basis. Treatment o f boundary conditions is simplified in this sparse point representation (SP R). Numerical examples are presented for one- and two-dimensional problems. It is found that the proposed method outperforms a finite difference metho d on a uniform grid for certain problems in terms of flops.