Sequential and Localized Implicit Wavelet Based Solvers for Stiff Partial Differential Equations

Abstract

This thesis explains and tests a wavelet based implicit numerical method for the solving of partial differential equations. Intended for problems with localized small-scale interactions, the method exploits the form of the wavelet decomposition to divide the implicit system created by the time discretization into multiple, smaller, systems that can be solved sequentially. Included are tests of this method on linear and non-linear problems, with both its results and the time required to calculate them compared to basic models. It was found that the method requires less computational effort than the high resolution control results. Furthermore, the method showed convergence towards high resolution control results.