Adaptive Wavelet Methods for Hyperbolic PDEs

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Abstract

We analyze 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 multidimensional analogue of the fast wavelet transform is used to expand the operators. We solve the advection equation and Burgers' equation on a periodic domain.

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