Study of Wavelet-Galerkin Solution and Its Application
Bing Li · Mechanical Science and Technology · 2003
We present an algorithm for solving a sort of singular differential equation, based on Wavelet Galerkin solutions (WGS). The general form of algorithm is presented in details. In order to overcome the integral difficulty that the Daubechies wavelet scaling functions have no explicit expression, we propose coefficients matrix and a general format to WGS variation by employing two scale equations and normalization condition arising from moment equations satisfied by wavelet. Considering the Dirichlet boundary condition, a periodic hypothesis that elliptic differential equation is only restricted by periodic boundary condition that source function and the right hand side function are periodic, convolution integral of periodic solution is gained. Dirichlet boundary conditions are then imposed, the solutions are localized in domain of definition by using the capacitance matrix, so that we may obtain an initial coarse description of the solution with little computational effort by means of analyzing periodic solutions, successively refine the solution in regions of interest with a minimum of extra effort. An example of transient thermal field solution for office paper indicates that WGS has desirable precision.