189	1996	Mats Holmström	matsh@tdb.uu.se	Solving Hyperbolic PDEs Using Interpolating Wavelets

                            Abstract


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 thresholding the wavelet coefficients.  Operations
such as differentiation and multiplication are fast and simple due to
the one-to-one correspondence between point values and wavelet
coefficients in the interpolating basis.  Treatment of boundary
conditions is simplified in this sparse point representation.
Numerical examples are presented for one- and two-dimensional
problems.  It is found that the underlying finite difference method's
order of convergence is preserved, and that the proposed method
outperforms a finite difference method for certain problems in terms
of flops.