Abstract:Meshless method is one kind of powerful tool for numerical solutions of partial differential equations (PDEs),and it has local technique and element-free characteristics. Among the meshless methods,moving least-square approximation is most common in constructing the shape function. The meshless method has more computation advantages in such respects as accuracy and pre-processing,post-processing,etc.. The paper introduces in detail the MLS technology and the interpolation characteristics,especially the MLS interpolation of singular weighted function. The Dirichlet boundary conditions are met through the use of a set of IMLS. Thus the Lagrange multipliers are eliminated. The validity,accuracy and efficiency of the method are demonstrated by comparing the results from IMLS with closed-form ones and the ones from FEM in 1D,2D examples.