Construction Interpolating Scaling Function With Lifting For Solution Of The Boundary Value Problems

On the ground of multiresolution analysis, Wavelet Galerkin Method uses wavelet scaling function as the basis for the resolution space, with whose linear combination any function in this space can be expressed. Then the Partial Differential Equations(for short PDEs) can be dispersed to a linear system through Galerkin. In this paper, we supply the generic form of elliptic problem in PDEs boundary value problems(for short boundary value problems), and explain how to disperse this type PDEs to a linear system.In order to constructing a basis for the resolution space, we introduce the theory and process of Lifting theme, a new method of constructing wavelet. With it, we can construct symmetric interpolating scaling function and its relevant average-interpolating scaling function with support. The former's 1st derivative can be computed with the latter. In this paper , we use the symmetric interpolating scaling function as the basis for the resolution space.The specialty of Wavelet Interpolation Galerkin Method(WIGM) is : the wavelet coefficients are the values of function at the equinoxes because of the character of interpolation of the basis function. So the method for solution of the boundary value problems is simple and effective. In this paper, we discuss how to solve the 1st, 2ed and composite boundary problem, add external wavelet to reduce the error. And we give method how to solve the problem when there are more than one kind of medium or the boundary is abnormity. Because using symmetric interpolating seal function as the Kisis con'pMied by its rele^a'it average-interpolating scaling function, the error can be less than computed by traditional method. There are many examples in the paper, which can explain how to use WIGM and prove the availability of the method by the analysis of the computed result.