A rational spectral collocation method for third-order singularly perturbed problems

被引：8
作者：
Chen, Suqin [1 ]
Wang, Yingwei [2 ]
机构：
[1] Tongji Univ, Dept Math, Shanghai 200092, Peoples R China
[2] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2016年 / 307卷
基金：
美国国家科学基金会;
关键词：
Third-order singularly perturbed problems; Rational spectral collocation method; Boundary layer; Asymptotic expansion; BOUNDARY-VALUE-PROBLEMS; DIFFERENTIAL-EQUATIONS; PSEUDOSPECTRAL METHOD; COMPUTATIONAL METHOD; PERTURBATIONS;
D O I：
10.1016/j.cam.2016.03.009
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A new numerical method is developed for solving a class of third-order singularly perturbed boundary value problems. First of all, the given problem is transformed into a system of two ordinary differential equations (ODEs) subject to suitable initial and boundary conditions. Then, the rational spectral collocation method in barycentric form with sinh transformation is applied to solve the system of ODEs. According to the asymptotic analysis, the location and width of boundary layer of the given problem, which are chosen as parameters in the sinh transformation, can be determined. Ample numerical experiments are presented to illustrate the computational efficiency and accuracy of the our method. (C) 2016 Elsevier B.V. All rights reserved.
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页码：93 / 105
页数：13
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