同伦摄动法在求解四阶边值问题中的应用  

Homotopy Perturbation Method for Solving Fourth-order Boundary Value Problem

作　　者：姜兆敏[1] 刘海玉[1] 黄金城[2] 李晓静[1] 

机构地区：[1]江苏理工学院数理学院,江苏常州213001 [2]河海大学常州校区数理部,江苏常州213022

出　　处：《数学的实践与认识》2015年第21期215-220,共6页Mathematics in Practice and Theory

基　　金：江苏理工学院青年科技基金项目(KYY11086);河海大学中央高校科研业务费项目(2013B09914)

摘　　要：将同伦摄动法用于求解常微分方程四阶边值问题.通过将常微分方程边值问题转化为积分方程组,应用同伦摄动法求得近似解.给出同伦摄动法在两个具体的实例中的应用,并将近似解与精确解进行了比较,验证了同伦摄动法对求解线性、非线性常微分方程边值问题是一种非常有效的方法.In this paper, we apply the homotopy perturbation method to solve the fourth- order boundary value problems by reformulating them as an equivalent system of integral equations. The analytical results of the system of integral equations have been obtained in terms of convergent series with easily computable components. Two examples are given to illustrate the efficiency and implementation of the homotopy perturbation method. Compar- isons are made to confirm the reliability of the homotopy perturbation method to solve the linear and nonlinear boundary value problems.

关 键 词：同伦摄动法 四阶边值问题 近似解 精确解 

分 类 号：O175.8[理学—数学]