矩阵微分方程通解的待定矩阵法  

Undetermined matrix method for the general solution of matrix differential equation

作　　者：吴幼明[1] 梁丽枝[1] 吴文峰 

机构地区：[1]佛山科学技术学院数学系,广东佛山528000 [2]爱荷华威斯莱大学商业管理系,爱荷华芒特普莱森特52641

出　　处：《佛山科学技术学院学报（自然科学版）》2016年第2期1-4,16,共5页Journal of Foshan University(Natural Science Edition)

基　　金：广东省自然科学基金资助项目(S2013010012463)

摘　　要：基于矩阵微分方程理论,采用待定矩阵方法,推导了非齐次项为三角函数与指数函数乘积的一类常系数矩阵微分方程的通解公式。进行了2种特殊情况的讨论,利用算例验证矩阵微分方程通解公式的正确性。丰富了矩阵微分方程的解法理论。Based on matrix differential equation theory, and by the method of undetermined matrix, the paper isdevoted to provide a general solution of finding a kind of matrix differential equation with constant coefficients,and the non-homogeneous terms of matrix differential equation are the form of the trigonometric functionsmultiplied by exponential function. The special cases are discussed in detail. For example, the general solutionformulas are validated. It is shown that the present method of solving on matrix differential equation is effectiveand general.

关 键 词：矩阵微分方程 待定矩阵方法 通解 

分 类 号：O151.21[理学—数学]