Rsearch And Application Of Wavelet Meshless Method Based On The Weighted Residual Method With Compactly Supported Trial Function

In this paper, based on the research of the multi-resolution analysis, using themulti-resolution analysis, combined with the nature of the scaling function, the differentspace on the structure of the orthonormal wavelet method were discussed, and for theconcrete multiresolution analysis, we present the corresponding wavelet constructionmethod to illustrate the feasibility of the method to construct. In addition, we alsoanalyzed the form of the trial function weighted residual method which was applied inthe meshless method, gives several different tight trial function weighted residual method,and the format of the Galerkin meshless method based on the moving least squares and itsapplicable conditions are presented. Through the study of wavelet theory of meshlessmethod, we present the wavelet construction method of meshless method on differentspace, and using the theory of compact integral operator, we get integral operatorexpression for the solution of the Sturm Liouville boundary value problem. In addition, wealso give the integral operator discretizationa discretization algorithm (BCR). Finally, weapply wavelet base constructed by the Battle-LeMarie method on the square integrablespace in meshless method, and get the Wavelet Galerkin format to solve the eigenvalueproblem of integral operator triggered by partial differential equations in classical physicsSturm Liouville boundary value problems, and analyze the convergence of the algorithm.Through the above theoretical analysis and example, we get the following conclusion:using wavelet Galerkin method to approximate solution of the eigenvalue concerning thecompact integral operator triggered by Sturm Liouville boundary value problem. Due tothe compactly supported wavelet, the numerical matrix is sparse (most of the element isnegligible), and the amount of calculation are reduced, thus this provide convenience forsolution of the eigenvalue, and through the theory the convergence of eigenvalues isproved.