Construction Of Orthogonal Wavelet Bases And Its Application In Numerical Solution Of Parabolic Equations

In the traditional methods for the numerical solution of parabolic differential equations,we usually discretize the spatial variables first,and then apply a difference approach in the time dimension. Recently,some foreign scholars have developed a new method for the numerical solution of PPDEs.As the first step,the method uses wavelet bases to decompose the forcing term,so the problem is transformed into some elliptic PDEs which can be solved by parallel algorithm. The new method has high computational efficiency and is suitable for parallel computing,but it is very complex to construct the suitable wavelet bases in time direction. In this paper,we will construct a class of Orthogonal Wavelet Bases,and present the general recurrence formula of wavelet coefficients.This paper is organized as follow. In chapter 1 we introduce the problem studied in this paper. Chapter 2 reviews the theoretical framework about discretization of parabolic problems in time direction by orthogonal wavelet bases.Chapter 3 is about the construction of Orthogonal Wavelet Bases;we give some concrete examples and deduce the general recurrence formula of wavelet coefficients .In chapter 4 we present the fast methods to parabolic problem with a spatial finite element semi- discretization and the construction of L~2 orthogonal bases with one and second order acuu-rate.