Duhamel原理在求解非齐次微分方程中的应用  

Application of Duhamel Principle to Non-homogeneous Differential Equations

作　　者：何家维 HE Jiawei(School of Mathematics and Information Science,Guangxi University,Nanning 530004,China)

机构地区：[1]广西大学数学与信息科学学院,广西南宁530004

出　　处：《高等数学研究》2024年第4期100-104,共5页Studies in College Mathematics

基　　金：高等学校大学数学教学研究与发展中心教改项目(CMC20220210).

摘　　要：本文围绕Duhamel原理在求解非齐次微分方程中的应用展开探讨.基于比较法,以常微分方程实例与偏微分方程实例为切入点,证明了相关Duhamel原理及推导出对应问题的解,结果的比较可使学生对求解方法更为印象深刻,并能将该原理灵活应用于求解各类非齐次的微分方程.In this paper,we discuss the application of non-homogeneous differential equations by using the Duhamel principle.Based on the comparison method,we prove the relevant Duhamel principles and the solutions for ordinary differential equations and partial differential equations.The comparison of results can make students more impress by the method,and they can flexibly apply the method to solve other types of non-homogeneous differential equations.

关 键 词：非齐次微分方程 Duhamel原理 比较法 

分 类 号：O171[理学—数学]