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一类二阶常系数非齐次线性微分方程及边值问题的解法
引用本文:李培超,李培伦,黎波,葛良燕.一类二阶常系数非齐次线性微分方程及边值问题的解法[J].数学的实践与认识,2011,41(3).
作者姓名:李培超  李培伦  黎波  葛良燕
作者单位:1. 上海工程技术大学,机械工程学院,上海,201620
2. 中国石油大学(华东)石油工程学院,山东,青岛,266555
基金项目:上海高校选拔培养优秀青年教师科研专项基金(gid09029); 上海工程技术大学大学生创新活动计划项目“一类物理问题的数学模型求解及工程应用”
摘    要:利用非齐次方程通解方法和Green函数法给出了非齐次项为点源函数的二阶常系数线性常微分方程及边值问题的求解方法和公式.然后以渗流力学一类具体问题为例进行了论证.结果表明这两种方法在本质上是一致的,所得到的结果是相互吻合的.该点源解可用于分析相关边值问题,并可用来求解具有一般非齐次项的微分方程及相关定解问题.

关 键 词:点源函数  非齐次方程特解  Green函数法  边值问题

The Solution of a Particular 2nd-order Nonhomogeneous Linear Ordinary Differential Equation with Constant Coefficients and Boundary Value Problem
LI Pei-chao,LI Pei-lun,LI Bo,GE Liang-yan.The Solution of a Particular 2nd-order Nonhomogeneous Linear Ordinary Differential Equation with Constant Coefficients and Boundary Value Problem[J].Mathematics in Practice and Theory,2011,41(3).
Authors:LI Pei-chao  LI Pei-lun  LI Bo  GE Liang-yan
Institution:LI Pei-chao~1,LI Pei-lun~2,LI Bo~1,GE Liang-yan~1 (1.School of Mechanical Engineering,Shanghai University of Engineering Science,Shanghai 201620,China) (2.School of Petroleum Engineering,China University of Petroleum(East China),Qingdao 266555,China)
Abstract:Utilizing methods of general solution and Green's function,the solution of a 2~(nd)-order linear ordinary differential equation(ODE) and the corresponding boundary value problem with a nonhomogeneous term in the form of point source function is presented.Then it is validated by a practical problem in the field of porous media flow.It indicates that the above two methods are consistent with each other in essence.The presented solution is of great use to analyze the relevant boundary value problems.Moreover,t...
Keywords:point source function  particular solution of nonhomogeneous linear ODE  Green's function method  boundary value problem  
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