Abstract: This paper presents a finite point method based on
directional derivatives for diffusion equation on 2D scattered points.
To discretize the diffusion operator at a given point, a six-point stencil
is derived by employing explicit numerical formulae of directional
derivatives, namely, for the point under consideration, only five
neighbor points are involved, the number of which is the smallest for
discretizing diffusion operator with first-order accuracy. A method for
selecting neighbor point set is proposed, which satisfies the solvability
condition of numerical derivatives. Some numerical examples are
performed to show the good performance of the proposed method.