数值处理奇性奇摄动边值问题  

Numerical treatment of singular-singularly perturbed boundary value problems

作　　者：张蕊蕊[1] 陈松林[1] ZHANG Rui-rui;CHEN Song-lin(School of Mathematics & Physics, Anhui University of Technology, Ma’anshan Anhui 243032, China)

机构地区：[1]安徽工业大学数理科学与工程学院,安徽马鞍山243032

出　　处：《阜阳师范学院学报（自然科学版）》2017年第1期4-7,共4页Journal of Fuyang Normal University(Natural Science)

摘　　要：采用了数值积分方法求解带有奇性的奇摄动边值问题,将原边值问题的一般方程近似转换为带有极小偏差的一阶微分方程,利用梯形公式得出三对角方程组,再采用修正的方法对奇性进行处理,得出新的三对角系统,最后利用追赶法解出三对角方程组并验证该方法的一致有效性.A numerical integration method is used to solve the singular-singularly perturbation boundary value problem.General equation of the original boundary value problem is transformed to an asymptotically equivalent first order differential equation with a small deviating argument.Tridiagonal system was obtained by applying Trapezoidal formula on the first order differential equation.Using the modified method to deal with the boundary value problem of singularity.Finally,we solved the tridiagonal equations by the catch-up method and verified the validity of the proposed method.

关 键 词：两点边值 数值积分 奇点 边界层 一致有效性 

分 类 号：O175.6[理学—数学] O175.8[理学—基础数学]