Supported by a Small Grant for Exploratory Research, a numerical investigation will be carried out to evaluated the utility of wavelet transforms in constructing solutions of partial differential equations. As a test problem, an available two-dimensional but steady state solution of Burgers equation will be used as a test bed. This is a prototype equation containing many of the characteristics exhibited by fluid motion, particularly localized regions with strong gradients. Wavelet-based numerical solutions will be compared to those from conventional techniques for this test case in which the results are known exactly. Wavelets contain a potential for more efficient and accurate numerical methods to predict complex fluid motions, applicable in diverse areas of engineering.
