数学物理方程中的分离变量法

Method of separation of variables is a general way to solve initial-boundary value problems of various types of linear partial differential equations. This paper studies the general approach to solve the initial-boundary value problem of bounded string vibration equation and one dimensional heat equation and the equation that the eigenvalue parameter satisfy is given. In the case of non-homogeneous equation with non-homogeneous boundary conditions, the series solution is also given by using the principle of superposition. Meanwhile, this paper also discuss the Sturm-Liouville eigenvalue problem which is the theoretical basis of method of separation of variables,and finally,the existence of classical solutions is verified by giving the functions which have been known certain conditions.