Date of Award:

2016

Document Type:

Dissertation

Degree Name:

Doctor of Philosophy (PhD)

Department:

Mathematics and Statistics

Advisor/Chair:

Joseph Koebbe

Abstract

This paper considers some numerical schemes for the approximate solution of conservation laws and various wavelet methods are reviewed. This is followed by the construction of wavelet spaces based on a polynomial framework for the approximate solution of conservation laws. Construction of a representation of the approximate solution in terms of an entropy satisfying Multiresolution Analysis (MRA) is defined. Finally, a proof of convergence of the approximate solution of conservation laws using the characterization provided by the basis functions in the MRA will be given.

Checksum

4e35fde1d8f96ec3c94c85fd891d71f0

Included in

Mathematics Commons

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