Stability estimate on meshless unsymmetric collocation method for solving boundary value problems

We investigate in this paper the stability of meshless unsymmetric collocation method by using radial basis functions for solving boundary value problems under Dirichlet, Neumann, or Robin boundary conditions. Using the monotonically decreasing property of the Fourier transforms of RBFs, we prove that the lowest bound of the resultant linear system depends on the separation distance of distinct centers and the decreasing order of the RBFs. Stability estimates can then be obtained for the meshless unsymmetric collocation method. For verification, several numerical examples are constructed to verify the theoretical results.