• 论文 •

### 关于热传导方程半离散差分格式的一个注记

1. 电子科技大学数学科学学院, 成都 611731
• 收稿日期:2014-10-21 出版日期:2015-11-15 发布日期:2015-11-19
• 基金资助:

国家自然科学基金(11101071,61472462)和国家公派留学基金([2012]3022)资助项目.

Li Houbiao, Zhong Erjie. A note on semi-discrete difference schemes of heat conduction equations[J]. Mathematica Numerica Sinica, 2015, 37(4): 401-414.

### A note on semi-discrete difference schemes of heat conduction equations

Li Houbiao, Zhong Erjie

1. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
• Received:2014-10-21 Online:2015-11-15 Published:2015-11-19

In this paper, based on semi-discrete difference scheme, a new direct algorithm on heat conduction equations is presented. For the Dirichlet and Neumann boundary conditions, the ordinary differential equations are derived from spatial difference scheme, and then the semi-analytical solution of original equation is obtained by the sine or cosine transforms. The corresponding convergence is also analyzed. The precision analysis on central difference and compact difference schemes is also presented by the corresponding eigenvalue theory. In addition, this direct algorithm may be directly developed into double sine or cosine transforms for two-dimensional heat conduction equations by the matrix tensor product. Since there does not exist the time discrete such that it has very high computational efficiency.

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