| 摘要: |
| 研究了具有长方系数矩阵的微分代数方程组的数组稳定性.利用克罗尼克标准型将原系统等价转化，获得了线性多步法和龙格-库塔法求解系统时的渐近稳定性结果. |
| 关键词: 长方系数矩阵 微分代数方程 渐近稳定 矩阵束 克罗尼克标准型 |
| DOI：10.3969/J.ISSN.1000-5137.2021.03.002 |
| 分类号:O241.81 |
| 基金项目:The Scientific Computing Key Laboratory of Shanghai Normal University and the Shanghai Natural Science Foundation (15ZR1431200) |
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| Asymptotic stability of linear multistep methods and Runge-Kutta methods for homogeneous differential-algebraic equations with rectangular coefficients |
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SUN Leping
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Mathematics and Science College, Shanghai Normal University, Shanghai 200234, China
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| Abstract: |
| This paper is concerned with the asymptotic stability of numerical methods applied to linear differential-algebraic equations. The coefficient matrices of the system are constant rectangular matrices. We consider linear multistep methods and Runge-Kutta methods applied to the system. The stability results are established under Kronecker canonical form of the original system. |
| Key words: rectangular coefficient matrix differential-algebraic equations asymptotic stability pencil Kronecker canonical form |
