自共轭常微分算子特征值的一种基于分离特征参数的数值解法

摘要

该文发现了特征方程ly(x,λ)=λy(x,λ)一般解的一种关于特征参数λ的幂级数表示及其求解方法,借此给出了自共轭常微分算子特征值的一种新的数值解法,并给出了算法的稳定性分析和误差估计.最后,通过数值实例来说明该算法是有效的.%In this paper, a power series representation in A and its method to solve for the general solution of eigen-equation ly(x, A) = Xy(x, A) are discovered. Then, a new numerical method to get eigenvalues of self-adjoint ordinary differential operators is obtained. Also the analysis of stability and error for the algorithm are given. At last, the numerical examples are presented to verify the efficiency of the method.