奇摄动拟线性边值问题的高阶近似解  

Higher Order Approximate Solutions of Singularly Perturbed Quasiliear Boundary Value Problems

作　　者：孔伟应 陈怀军 娄正来 KONG Wei-ying;CHEN Huai-jun;LOU Zheng-lai(School of Mathematics and Statistics,Anhui Normal University,Wuhu 241000,China)

机构地区：[1]安徽师范大学数学与统计学院,安徽芜湖241000

出　　处：《安徽师范大学学报（自然科学版）》2019年第1期22-27,共6页Journal of Anhui Normal University(Natural Science)

基　　金：国家自然科学基金(11301007)

摘　　要：研究了一类具有边界层性质的奇摄动拟线性边值问题。在相对较弱的条件下,利用合成展开法构造问题的形式近似解,然后利用不动点定理证明解的存在性,并给出满足边界层性质的高阶近似解,使得它与精确解之间的渐近估计可达到任意O(ε~n)阶近似。Some singularly perturbed quasilinear boundary value problems with boundary layer properties are studied.Under the weaker conditions,the formal approximation of the problem is constructed using the method of composite expansions.The existence of solutions are proved and a higher order approximate solution of the problem is gained by the fixed point theorem.It is shown that an asymptotic estimation of any order O(ε n) approximation is achieved between the exact solution and approximate solution.

关 键 词：奇摄动 边值问题 合成展开法 高阶近似 不动点定理 

分 类 号：O175.14[理学—数学]