小波配置法中对边界处理的改进

IMPROVEMENT OF THE BOUNDARY TREATMENT FOR THE WAVELET COLLOCATION METHOD

提出了小波配置法中第二类边界条件的处理方法 ,且引入外小波的概念 ,使该方法进一步改进 ,有效地降低了计算的复杂度 ,并将此方法应用到求解静电场中的二维偏微分方程 。

According to the classic method of weighted residuals,a wavelet collocation method is a new method for the numerical solution of partial differential equations by constructing a wavelet trial function with Daubechies’ compactly supported and orthogonal wavelet,which has the feature of interpolating function,based on the multiresolution analysis.The paper presents the treatment of the second boundary condition in the wavelet collocation method and introduces the concept of external wavelets to improve the method so as to decrease the degrec of complexity of computing efficiently,and the wavelet collocation method is applied to solve 2 dimensional partial differential equations in static electronic field,and satisfactory data are obtained.