Global meshless methods based on radial basis functions for solving eigenvalue problems in Partial differential equations

Global meshless methods based on radial basis functions for solving eigenvalue problems in Partial differential equations

In this paper, we develop some meshless methods based on radial basis functions (RBFs) for solving eigenvalue problems in Partial differential equations as well as Steklov eigenvalue problems. The global methods that we employed here, including the RBF collocation method (RBFCM), method of approximate particular solution (MAPS) and Hermite RBF collocation method (HRBFCM). Moreover, we develop a new method based on Hermite interpolation to modify the MAPS. We also compare the performance of these methods by applying them to eigenvalue problems subjected to different boundary conditions and also with the eigenvalue appearing in the governing equation or in the boundary conditions