Wavelet Analysis In Solving Ordinary Differential Equations

Wavelet analysis theory is a arisen science which was applied extensively to every domain. Being a time-frequency analysis tool in 1980s', wavelet transform has succeeded to be applied to the signal and image processing domain and been the criterion of JPEG 2000 by it's advantages. Based on Multiresolution Analysis, scale functions and wavelet functions have good analysis and computation characteristic which are been made the best of to discrete the differential equations. Then some algebra equations can be acquired. The method is named of wavelet finite element method has attracted many scholars' interests.In this paper, after wavelet analysis theory being discussed clearly, the multiresolution analysis of M-band multiwavelet theory is introduced which contributed to multiresolution filter banks. The application of wavelet used to the solution of ordinary differential equations (ODE) and a modified algorithm which resolves ODE is proposed. After ODE being a discrete algebra equation systems by wavelet, the best M term approximation idea is combined with the wavelet characteristics. And the iterate method of equation systems is modified. The computation is reduced, the improved algorithm contributes to the resolution of large equation systems. The feasibility and reasonability are proved by theory analysis and numerical experiments.