Computation of Two-Dimensional Poisson Equation Using the Third-Order Discrete Scheme of Finite Difference Method Based on Node Set Vector

A novel third-order discrete scheme of finite difference method based on node set vector for two dimensional Poisson equation is proposed in this paper. Studies on the basic discrete scheme of this method as well as the discrete scheme of the interior node and boundary node are carried out in detail. Computer programs are also developed to emulate a computation sample. The numerical computation results show that this discrete scheme is effective for the numerical computation of two dimensional Poisson equation.