摘要
本文改进了传统的使边界条件齐次化的公式,将一个待定函数引入公式,找到了下述两类方程中求解这一待定函数的方法。这一方法(以下简称待定函数法)用于求解波动方程和热传导方程的部分定解问题时,既能使边界条件齐次化,又可使原方程仍保持齐次方程形式。甚至可使相当一部分非齐次方程在边界条件齐次化的同时,变成齐次方程,从而给这两类数理方程在非齐次边界条件下的求解带来极大的方便。
This paper improves the customary formula of making the boundary condition convert into a homogenous one. By introducing an uncle termined function into the formula, a method of solving the undermined function can be found in the following two sorts of equations, When this method (called undetermined function method for short) is ustd to solve partial boundary value problems in the wave equation and the equation of heat conduction, it can not only convert the boundary condition Into a homogenous one but also can make the homogenous equation remain unchanged. Furthermore, if can make a considerable number of nonhomogenous equations homogenous at the time when boundary conditions are made homogenous. Thus great convenience has been brought about in solving the two sorts of equations of mathematical physics under nonhomogenous boundary conditions.
出处
《重庆师范学院学报（自然科学版）》
1991年第4期49-56,共8页
Journal of Chongqing Normal University(Natural Science Edition)
关键词
数理方程
非齐次项
定解问题
equation of mathematic physics, nonhomogenous term, boundary value condition, unJeiermined function, solving boundary value problem, source function
