185	1996	Johan Walden	johan@tdb.uu.se	Filter Bank Methods for Hyperbolic PDEs


			Abstract

We use biorthogonal filter banks to solve hyperbolic PDEs adaptively with a sparse 
multilevel representation of the signal. The methods described are of finite difference 
type, and the filter banks are used to give a sparse representation of signals, and 
to transform between grids on different scales. We derive bounds for the error and number
 of coefficients in the sparse representation. These bounds also apply for filter banks 
that are not associated with any wavelets. We develop algorithms for fast differentiation
 and multiplication in detail. The strength of the method is shown in various test problems.