中文摘要：

这份报纸基于方向性的差别为有限的点方法使一些成为数学分析。由用仅仅为一阶的计算和秒顺序的五个附近的点的数字公式的明确的表达式的优点方向性的 differentials，新方法论被介绍给拉普拉斯算符操作符在 2D 上定义的 discretize 散布的点分布。有很弱的限制的一些足够的条件被获得，在哪个下面结果的计划是积极计划。作为后果，分离最大的原则被证明，并且第一命令 O (h) 的会聚的结果为在散布的点分布上定义的节的答案被完成，它能在一致的点分布上被提起直到 O (h2 ) 。

英文摘要：

This paper makes some mathematical analyses for the finite point method based on directional difference. By virtue of the explicit expressions of numerical formulae using only five neighboring points for computing first-order and second-order directional differ- entials, a new methodology is presented to discretize the Laplacian operator defined on 2D scattered point distributions. Some sufficient conditions with very weak limitations are obtained, under which the resulted schemes are positive schemes. As a consequence, the discrete maximum principle is proved, and the first order convergent result of O（h） is achieved for the nodal solutions defined on scattered point distributions, which can be raised up to O（h2） on uniform point distributions.