一类四阶常微分方程两点边值问题的奇摄动  

A Class of Singularly Perturbed Two-Point Boundary Values Problem for Fourth-Order Ordinary Differential Equation

作　　者：胡永生[1] HU Yong-sheng(College of General Education,Fujian Vocational College of Agriculture,Fuzhou Fujian 350007,China)

机构地区：[1]福建农业职业技术学院通识教育学院,福建福州350007

出　　处：《淮阴师范学院学报（自然科学版）》2022年第2期115-120,共6页Journal of Huaiyin Teachers College;Natural Science Edition

摘　　要：研究了一类四阶常微分方程两点边值奇摄动问题,分析其边界层行为.由匹配渐近展开法,构造了问题的外部解;通过引入伸展变换,构造边界层(内层)函数,获得内层解.通过Van Dyke匹配原则,将内外解进行匹配,得到奇摄动问题的一致有效的复合解.最后,通过数值解验证了结果的正确性.The two-point boundary value singularly perturbed problem for a class of fourth-order ordinary differential equations is studied.The external solution of the problem is constructed by the asymptotic expansion method;By introducing the stretching transformation,the boundary layer function is obtained.Finally,through the Van Dyke matching principle,the outer and inner expansion are matched to obtain the uniformly effective composite expansion of the singularly perturbed problem.The correctness of the result is verified by numerical solution.

关 键 词：四阶常微分方程 边界层 特异极限 Van Dyke匹配原则 

分 类 号：O175.8[理学—数学]