Physical Sciences and Mathematics Commons^™

Definition And Construction Of Entropy Satisfying Multiresolution Analysis (Mra), Ju Y. Yi

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

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.