关键词: 导热微分方程, 配点型无网格法, 无网格迭代求解法

Abstract: Collocation meshless method is applied to solve the heat conduction differential equations and an iterative meshless technique is proposed. The results show that the collocation meshless and iteration method is convenient in the implementation of programming, and the computation accuracy is almost the same as that of FEM. The iterative meshless method is free of assembling the interpolation matrix, and it only occupies a little storage space because of point iteration. By properly selecting a relaxation factor, the number of iterations can be decreased for the relaxation iterative method compared with the Gauss-Seidel iteration. The preliminary study indicates that collocation meshless and iteration method has advantage for solving large scale engineering problems.

Key words: Heat conduction differential equations, Iterative meshless technique, Collocation meshless method