线性常微分扰动方程的级数解空间分析

On Series Solution Space of Linear Ordinary Differential Perturbation Equation

用无限阶矩阵研究线性常微分扰动方程的幂级数解空间,发现加入非奇异扰动项后它的维数增加,但幂级数解的收敛半径一般不与扰动系数ε一起趋向零;并找到幂级数解的系数ε变化不大的一类奇异扰动方程。

The series solution space of the linear ordinary differential perturbation equation is studied with infinite order matrix. Its dimension is increased by non-singular perturbation. But the radius of convergence does not approach to zero along with the perturbation coefficient e. The singular perturbation equations whose coefficients of series solutions vary a fat lot are found.