A Finite Point Method Based on Directional Derivatives for Diffusion Equation

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.

Authors:

• Guixia Lv
• Longjun Shen

Keywords:

• Finite point method
• directional derivatives
• diffusionequation
• method for selecting neighbor point set.

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