| 摘要: |
| 本文研究了分段连续型微分方程x'(t)=ax(t)+bx(3[(t+1)/3]) Euler-Maclaurin方法的数值稳定性问题.利用特征分析的方法,获得了数值解稳定的充分条件,进而证明了Euler-Maclaurin方法保持了精确解的稳定性.最后给出了一些数值例子. |
| 关键词: Euler-Maclaurin方法 分段连续项 稳定性 数值解 |
| DOI： |
| 分类号:O241.81 |
| 基金项目:Supported by National Natural Science Foundation of China (11201084);China Postdoctoral Science Foundation (2013M531842) and Science and Technology Program of Guangzhou (2014KP000039). |
|
| NUMERICAL STABILITY ANALYSIS FOR EQUATION x'(t)=ax(t)+bx(3[(t+1)/3]) |
|
WANG Qi, WANG Xiao-ming, CHEN Xue-song
|
|
School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510006, China
|
| Abstract: |
| In this paper, we investigate the numerical stability of Euler-Maclaurin method for differential equation with piecewise constant arguments x'(t)=ax(t)+bx(3[(t+1)/3]). By the method of characteristic analysis, the sufficient conditions of stability for the numerical solution are obtained. Moreover, we show that the Euler-Maclaurin method preserves the stability of the exact solution. Finally, some numerical examples are given. |
| Key words: Euler-Maclaurin method piecewise constant arguments stability numerical solution |
