The comparison of three meshless methods using radial basis functions for solving fourth-order partial differential equations

In this paper we apply the newly developed method of particular solutions (MPS) and one-stage method of fundamental solutions (MFS-MPS) for solving fourth-order partial differential equations. We also compare the numerical results of these two methods to the popular Kansaʹs method. Numerical results in the 2D and the 3D show that the MFS-MPS outperformed the MPS and Kansaʹs method. However, the MPS and Kansaʹs method are easier in terms of implementation.