对流扩散方程的点插值无网格算法

Piont Interpolation Meshless Method of Convection-diffusion Equation

介绍了点插值原理,针对一维对流扩散方程构造带有多项式基的径向点插值无网格方法,证明了解的存在唯一性,并对具体对流扩散方程沿特征线进行无网格计算,计算结果表明,新算法结构简单,计算精度高。

A radial point interpolation meshless method with polynomial basis is a new numerical method. In this paper, the basic principle of this method is introduced, and meshless method is combined with method of characteristics, which is applied to one-dimensional convection-diffusion equation. Existence and uniqueness of solution is proved. Finally, the numerical results show that this procedure is simple and effective.