Coupling of high order multiplication perturbation method and reduction method for variable coefcient singular perturbation problems  

作　　者：张文志 黄培彦 

机构地区：[1]School of Civil and Transportation Engineering,South China University of Technology

出　　处：《Applied Mathematics and Mechanics(English Edition)》2014年第1期97-104,共8页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Key Program)(Nos.11132004 and 51078145)

摘　　要：Based on the precise integration method （PIM）, a coupling technique of the high order multiplication perturbation method （HOMPM） and the reduction method is proposed to solve variable coefficient singularly perturbed two-point boundary value prob lems （TPBVPs） with one boundary layer. First, the inhomogeneous ordinary differential equations （ODEs） are transformed into the homogeneous ODEs by variable coefficient dimensional expansion. Then, the whole interval is divided evenly, and the transfer ma trix in each sub-interval is worked out through the HOMPM. Finally, a group of algebraic equations are given based on the relationship between the neighboring sub-intervals, which are solved by the reduction method. Numerical results show that the present method is highly efficient.Based on the precise integration method （PIM）, a coupling technique of the high order multiplication perturbation method （HOMPM） and the reduction method is proposed to solve variable coefficient singularly perturbed two-point boundary value prob lems （TPBVPs） with one boundary layer. First, the inhomogeneous ordinary differential equations （ODEs） are transformed into the homogeneous ODEs by variable coefficient dimensional expansion. Then, the whole interval is divided evenly, and the transfer ma trix in each sub-interval is worked out through the HOMPM. Finally, a group of algebraic equations are given based on the relationship between the neighboring sub-intervals, which are solved by the reduction method. Numerical results show that the present method is highly efficient.

关 键 词：high order multiplication perturbation method （HOMPM） reductionmethod variable coefficient singular perturbation problem two-point boundary valueproblem 

分 类 号：O175.8[理学—数学] O241.81[理学—基础数学]