具有长方系数矩阵的微分代数方程组数值解的渐近稳定性  

Asymptotic stability of linear multistep methods and Runge-Kutta methods for homogeneous differential-algebraic equations with rectangular coefficients

作　　者：孙乐平[1] SUN Leping(Mathematics and Science College,Shanghai Normal University,Shanghai 200234,China)

机构地区：[1]上海师范大学数理学院,上海200234

出　　处：《上海师范大学学报（自然科学版）》2021年第3期280-290,共11页Journal of Shanghai Normal University(Natural Sciences)

基　　金：The Scientific Computing Key Laboratory of Shanghai Normal University and the Shanghai Natural Science Foundation(15ZR1431200)。

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.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.

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 

分 类 号：O241.81[理学—计算数学]