摘要
本文利用张量分析给出了常系数线性常微分方程组和n阶常系数线性常微分方程初值问题一般解的显式表示,包括特征根有重根时的情况.实际上本文给出了计算矩阵exp[At]的元素的一般公式.这种方法不仅在公式表示上简洁方便,而且更适用于计算机的程序设计,大大加快了运算速度.
In this paper by using tensor analysis we give the explicit expressions of the solution of the initial-value problem of homogeneous linear differential equations with constant coefficients and the nth-order homogeneous linear differential equation with constant coefficients. In fact, we give the general formula for calculating the elements of the matrix e, We also give the results when the characteristic equation has the repeated roots. The present method is simpler and better than the other methods
出处
《应用数学和力学》
CSCD
北大核心
1992年第12期1069-1074,共6页
Applied Mathematics and Mechanics
关键词
显式解
常微分方程
线性
tensor differential equation, characteristic tensor, explicit solution