The purpose of this project is to develop solution methods for initial and/or boundary value problems for differential equations based on the recently discovered compactly supported wavelet basis functions. An additional purpose is to continue the investigation of the theoretical and numerical properties of wavelets. The first phase will investigate the problem of linear and nonlinear one and two-dimensional scalar equations to determine the feasibility of using wavelets to solve differential equations. Later phases will include vector-valued problems arising in fluid dynamics, field theory and finite elasticity. Phase III will develop commercially usable computer programs for wavelet-based solutions to partial differential equations for practical applications.
