Stable and Convergent Unsymmetric Meshless Collocation Methods

In the theoretical part of this paper, we introduce a simplified proof technique for error bounds and convergence of a variation of E. Kansa’s well-known unsymmetric meshless collocation method. For a numerical implementation of the convergent variation, a previously proposed greedy technique is coupled with linear optimization. This algorithm allows a fully adaptive on-the-fly data-dependent meshless selection of test and trial spaces. The new method satisfies the assumptions of the background theory, and numerical experiments demonstrate its stability. Kansa’s method, convergence, error bounds, linear optimization, minimax algorithms