第一、二、三类非齐次线性边界条件的齐次化  

Homogenizing for Linear Non-Homogeneous Boundary Conditions of Class 1, 2 or 3

作　　者：陆立柱[1] 

机构地区：[1]太原师范学院物理系,山西太原030001

出　　处：《山西师范大学学报（自然科学版）》2001年第4期17-20,共4页Journal of Shanxi Normal University(Natural Science Edition)

摘　　要：本征函数法和格林函数法是求解数学物理定解问题的常用方法 ,这些方法要求问题具有齐次线性边界条件 .若定解问题具有非齐次线性边界条件 ,则必须选择辅助函数 ,使之化为齐次边界条件 .本文首先对稳定的非齐次边界条件进行讨论 ,得到选择辅助函数的普遍方法和结果 ;然后对其结果应用参数变易法进行改造 ,使之适用于不稳定的非齐次边界条件 ,从而得到选择辅助函数的普遍方法和结论 .Eigenfunction and Green′s function are the main methods to get the definite solutions of Mathematical physics problems, but the problem should have linear homogeneous conditions. If the problem has the non-homogeneous boundary conditions, an auxiliary function should be found to transfer it to be under the conditions of homogeneous boundary conditions. In the paper, firstly we discuss problems of stable non-homogeneous boundary conditions to get the general method and results of how to select the auxiliary function; then transform the results by transformation of parameter, and verify the results is applicable to problems of unstable non-homogeneous border conditions. At last we get the general method and solution to select an auxiliary function.

关 键 词：非齐次线性边界条件 齐次化 参数变易法 稳定 不稳定 数学物理方法 辅助函数 

分 类 号：O411.1[理学—理论物理]