Kwok, Ting-On; Ling, Leevan On convergence of a least-squares Kansa’s method for the modified Helmholtz equations. (English) Zbl 1262.35093 Adv. Appl. Math. Mech. 1, No. 3, 367-382 (2009). Summary: 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. Cited in 10 Documents MSC: 35J25 Boundary value problems for second-order elliptic equations 65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs 65N15 Error bounds for boundary value problems involving PDEs 65N35 Spectral, collocation and related methods for boundary value problems involving PDEs Keywords:radial basis function; adaptive greedy algorithm; asymmetric collocation; Kansa’s method; convergence analysis Software:Matlab PDFBibTeX XMLCite \textit{T.-O. Kwok} and \textit{L. Ling}, Adv. Appl. Math. Mech. 1, No. 3, 367--382 (2009; Zbl 1262.35093)