Convergence analysis and detection of singularities within a boundary meshless method based on Taylor series

We study a meshless method based on Taylor series approximation. This method solves quasi-exactly the Partial Differential Equation (PDE) in the domain. The boundary conditions are applied by using a least square method as proposed by Zhang et al. (2001 [3]), for stabilising collocation method. After showing accuracy and efficiency of the technique, we analyse the convergence of the series. In this aim, we introduce techniques as Domb Sykes plot, Hadamard criterion or Darboux criterion. This analysis leads to the radius of convergence and to the location and the nature of the singularities of the sought solution.