A dynamically adaptive multilevel wavelet collocation method for solving partial differential equations in a finite domain

Abstract

A dynamically adaptive multilevel wavelet collocation method is developed for the solution of partial differential equations. The multilevel structure of the algorithm provides a simple wayto adapt computational refinements to local demands of the solution. High resolution computations are performed only in regions where sharp transitions occur. The scheme handles general boundary conditions. The method is applied to the solution of the one-dimensional Burgers equation with small viscosity, a moving shock problem, and a nonlinear thermoacoustic wave problem. The results indicate that the method is very accurate and efficient. © 1996 Academic Press, Inc.