On Convergence of a Least-Squares Kansa's Method for the Modified Helmholtz Equations

Abstract

We analyze a least-squares  asymmetric radial basis function collocation method for solving the modified Helmholtz equations. In the theoretical part, we proved the convergence of the proposed method providing that the collocation points are sufficiently dense. For numerical verification, direct solver and a subspace selection process for the trial space (the so-called adaptive greedy algorithm) is employed, respectively, for small and large scale problems.