关键词: 　小波尺度函数, 广义高斯积分, 误差分析, 函数逼近, 应用举例．

Abstract:

in this paper,a generalized Gaussian integral method is established to take calculation of intergral for decomposion  coefficients of the scaling function transform in the Daubechies wavelet theory.By using teh resolution level increases.After taht,an explicit formula of reconstruction of functions based on teh scaling function transform is deduced out.and some expressions are displayed to functional,differential and integral operations of functions.it is found that this method is powerful to solve for soulutions of strong nonlinear problems.finally,an example of a two-point boundary value problem with strong nonliearity is given to show the efficiency of teh method.

Key words: 　Ｓｃａｌｉｎｇｆｕｎｃｔｉｏｎｓｏｆｗａｖｅｌｅｔ, Ｇｅｎｅｒａｌｉｚｅｄ Ｇａｕｓｓｉａｎｉｎｔｅｇｒａｌ, Ｅｒｒｏｒｅｓｔｉｍａ
ｔｉｏｎ, Ａｐｐｒｏｘｉｍａｔｉｏｎｏｆｆｕｎｃｔｉｏｎｓ, ａｐｐｌｉｃａｔｉｏｎｓ．