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

详细信息    查看全文

• 作者：Suqin Chen^a ; ^{tjchensuqin@mail.tongji.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Yingwei Wang^b ; ^{wywshtj@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Third-order singularly perturbed problems ; Rational spectral collocation method ; Boundary layer ; Asymptotic expansion
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2016
• 出版时间：1 December 2016
• 年：2016
• 卷：307
• 期：Complete
• 页码：93-105
• 全文大小：563 K

文摘

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$sinh$ 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$sinh$ transformation, can be determined. Ample numerical experiments are presented to illustrate the computational efficiency and accuracy of the our method.