Least-Squares Collocation Points Meshless Method with Radial Basis Functions Solving Elliptic Equations

摘要

This paper proposes a least-squares collocation points meshless method with radial basis functions to solve elliptic equations. Firstly, based on the collocation meshless method with radial basis functions, a number of auxiliary points and boundary points are added to construct the overdetermined linear equations, then the least-squares method is used to solve the equations. Secondly, the existence and uniqueness of the proposed method are proved. Moreover, a permutation matrix is used for improving the accuracy while solving the overdetermined linear equations. The results of the examples show that the accuracy and stability of the proposed method are better than that of collocation.