Preprint: Unification of Computational Methods by Wavelets

[Wei Guowei (guowei@cz3.nus.edu.sg)]

#1 Preprint: Unification of Computational Methods by Wavelets

Title: Unification of Computational Methods by Wavelet

Authors: G. W. Wei, Department of Computational Science
National University of Singapore

This Letter addresses the unification of a number of computational
methods in the framework of a wavelet discrete singular convolution
algorithm. By adjusting kernel supports, the present approach
interplays between local and global methods. Three standard
approaches of the method of weighted residual, namely, the Galerkin,
collocation and subdomain, are put on an equal footing. Moreover, in
an appropriate setting, the present approach becomes generalized
finite difference and finite volume methods. A finite element method
is realized by a subdomain treatment. Some of the best numerical
results are obtained for the Schr"{o}dinger equation, the
Navier-Stokes equation and the Swift-Hohenberg equation.

Keywords: Unified computational methods;
Wavelet discrete singular convolution;