Precise integration method for solving singular perturbation problems  

作　　者：富明慧 张文志 S.V.SHESHENIN 

机构地区：[1]Department of Applied Mechanics and Engineering,Sun Yat-sen University [2]Faculty of Mechanics and Mathematics,Lomonosov Moscow State University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2010年第11期1463-1472,共10页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(No.10672194);the China-Russia Cooperative Project(the National Natural Science Foundation of China and the Russian Foundation for Basic Research)(No.10811120012)

摘　　要：This paper presents a precise method for solving singularly perturbed boundary-value problems with the boundary layer at one end. The method divides the interval evenly and gives a set of algebraic equations in a matrix form by the precise integration relationship of each segment. Substituting the boundary conditions into the algebraic equations, the coefficient matrix can be transformed to the block tridiagonal matrix. Considering the nature of the problem, an efficient reduction method is given for solving singular perturbation problems. Since the precise integration relationship introduces no discrete error in the discrete process, the present method has high precision. Numerical examples show the validity of the present method.This paper presents a precise method for solving singularly perturbed boundary-value problems with the boundary layer at one end. The method divides the interval evenly and gives a set of algebraic equations in a matrix form by the precise integration relationship of each segment. Substituting the boundary conditions into the algebraic equations, the coefficient matrix can be transformed to the block tridiagonal matrix. Considering the nature of the problem, an efficient reduction method is given for solving singular perturbation problems. Since the precise integration relationship introduces no discrete error in the discrete process, the present method has high precision. Numerical examples show the validity of the present method.

关 键 词：singular perturbation problem first-order ordinary differential equation two-point boundary-value problem precise integration method reduction method 

分 类 号：O241.4[理学—计算数学]