171 1995 Mats Holmstrom and Johan Walden johan@tdb.uu.se Adaptive Wavelet Methods for Hyperbolic PDEs Abstract We analyse how to solve hyperbolic PDEs with compactly supported orthonormal wavelets adaptively. We use thresholded wavelet expansions of signals and operators. A tree structure is used to represent the signal, and a multi-dimensional analogue of the fast wavelet transform is used to expand the operators. We solve the advection equation and Burgers' equation on a periodic domain.