Some Numerical Remarks on a Meshless Approximation Method

In this paper we consider sources of enhancement for the Smoothed Particle Hydrodynamics method in approximating a function and its derivatives. It is well known that the standard formulation is usually poor when scattered data distribution is considered or when the approximation near the boundary occurs. In this paper studies on the accuracy are provided and assessed with gridded and scattered data distribution in the problem domain. The improvements of the method are addressed and supporting numerical experiments are included.