ORTHONORMAL WAVELET BASES ADAPTED FOR PARTIAL-DIFFERENTIAL EQUATIONS WITH BOUNDARY-CONDITIONS

We adapt ideas presented by Auscher to impose boundary conditions on t he construction of multiresolution analyses on the interval, as introd uced by Cohen, Daubechies, and Vial. We construct new orthonormal wave let bases on the interval satisfying homogeneous boundary conditions. This construction can be extended to wavelet packets in the case of on e boundary condition at each edge. We present in detail the numerical computation of the filters and the derivative operators associated wit h these bases. We derive quadrature formulae in order to study the app roximation error at the edge of the interval. Several examples illustr ate the present construction.