Spline Interpolation Wavelets And Application

We investigate Spline Interpolation Wavelet and Application in this paper.A kinds of forth-order B-spline and quintic B-spline scaling function was showed,then we construct a wavelet by using quintic B-spline scaling function.and we discuss its application for SEBVP.This paper first presents the development of the wavelet analysis and its applications. Include applications for many domain, such as the signal domain, numerical computation of mathematics and so on. In particular, we present its applications on solve the PDEs by using a wavelet approximation.Next, we prepare some speculative knowledge for this paper, such as semi-power function,Multi-Resolution Analysis.And then, we investigate how to construct a semi-orthogonal wavelet.(1)We discuss some simple property of the space V_n (0,1)which span by a forth-order scaling function.(2)We construct a quintic spline Muli-Resolution analysis for the Sobolev space H₀² (I), where I is a bounded interval.Next we construct a quintic spline interpolation wavelet bases for the Sobolev space H₀² (I).Last,for it's simple application,it introduces the Riesz wavelet method and Newton's method to solve the SEBVP, which has a single solution.