| 一种基于完全线性变换法则的差分方程解析解算法 |
| |
| 作者姓名： | 宋记锋 葛运建 |
| |
| 作者单位： | 1.中国科学院合肥智能机械研究所仿生感知与控制研究中心，合肥 230031； ;2.中国科学技术大学自动化系，合肥 230027 ; |
| |
| 摘 要： | 利用传统方法很难在计算机上实现差分方程的解析解求解，本文提出了一种获得差分方程解析解的线性算法，该算法的基础是完全线形变化法。其核心操作为降维处理，对高阶差分方程进行逐次降阶运算，直至获得其解析解表达式。本质上，该算法属于Z变换法的一种矩阵法变形。算法的线性特征使得其容易移植到计算机上实现差分方程的解析解运算，而非传统的数值迭代解。
|
| 关 键 词： | 差分方程 解析解 降维 |
A linear algorithm based on complete linear transformation for analytic solution of difference equation |
| |
| Authors: | Song Ji-Feng Ge Yun-Jian |
| |
| Institution: | 1.Center for Biomimetic Sensing and Control Research Institute of Intelligent Machines ,Chinese Academy of Sciences, Hefei 230031, China;2.Department of Automation of University of Science and Technology of China, Hefei 230027, China ; |
| |
| Abstract: | It is difficult to get the analytic solution of difference equation by using traditional methods with computer. A linear method based on complete linear transformation for getting the analytic solution of difference equation is proposed in this paper. The idea of this new method is dimensionality reduction. The orders of the high-order difference equation are reduced through determinant calculation, and this process is repeated till the last analytic expression of the solution of the difference equation appears. In essence, this algorithm is a transformation of Z-transform method combined with linear algebra method. The linear property of this algorithm enables one to get analytic solution other than numerical solution of difference equations using computer. |
| |
| Keywords: | difference equations analytic expression dimensionality reduction |
|
| 点击此处可从《》浏览原始摘要信息 |
| 点击此处可从《》下载免费的PDF全文 |
