A meshless method based on Taylor series

Abstract

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. for stabilizing collocation method. Sometimes, the convergence can only be obtained by splitting the domain in to several subdomains: a new bridging technique is proposed to match several polynomial approximations. Finally, numerical techniques like the Domb Sykes plot permits us to estimate the radius of convergence of the series.