| Meshless method are relatively new numerical methods which have gained popular-ity in computation and engineering sciences during the two decades. Meanwhile, moreand more experts and scholars make attention to it. Because the most significant charac-teristic of meshless method is that it doesn’t need meshless and get rid of the initializationof the meshless and the constraints of meshless reconstruction, meshless method is a kindof very promising numerical method and have important research value.The main idea of the paper is to introduce some meshless methods based on radialbasis function, where the foundation is radial basis function and its radial basis functioninterpolation. in addition, the paper mainly introduce Kansa.s Method,the Method ofParticular Solutions(MPS), the Method of Fundamental Solutions(MFS), the one-stageof MFS-MPS and the two-stage of MFS-MPS, where the basic train of thought betweenKansa’s Method and MPS is relatively similar. Therefore, we separately ues Kansa’sMethod and MPS to solve a kind of two-dimensional heat conduction equation and wealso compare and analyse the results of them.The biggest characteristic of the Method of Fundamental Solution is choosing thefictitious boundary outside the boundary so that we can avoid the singularity of the sourcepoint. So we use MFS to solve a kind of partial diferential equation with complicatedboundary and the result is comparative ideal. Finally, the paper also introduce the one-stage of MFS-MPS and the two-stage of MFS-MPS, where the main idea of two methodsis much similar. But the biggest diference is that the one-stage of MFS-MPS makes twosteps to one step. Furthermore, the one-stage of MFS-MPS has been proposed to furtherimprove the MFS to be able to solve PDEs with variable coefcients, but the two-stage ofMFS-MPS can not. Meanwhile, we use these two methods to solve a kind of Poisson’sequation and compare the results of them. |
