Local meshless methods based on radial basis functions for eigenvalue problems in partial differential equations

Local meshless methods based on radial basis functions for eigenvalue problems in partial differential equations

This paper is concerned with the development of meshless methods using radial basis func- tions (RBFs) for eigenvalue problems in partial differential equations. The local methods that we employed here, including local method of approximate particular solution (LMAPS) and RBF finite difference (RBF-FD) method, which unlike the global methods yield sparse and well-conditioned matrices. In addition, we introduce a higher order version for LMAPS is referred to as Hermite LMAPS (HLMAPS). We analyze and compare the performance of these methods by applying them to eigenvalue problems subjected to different boundary conditions. Computational results and the graphi- cal representation of numerical solutions are presented to verify the accuracy of the presented methods.