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

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 spec...

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Bibliographic Details
Published inJournal of computational and applied mathematics Vol. 307; pp. 93 - 105
Main Authors Chen, Suqin, Wang, Yingwei
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.12.2016
Subjects
Asymptotic expansion
Asymptotic properties
Boundary layer
Collocation methods
Computational efficiency
Differential equations
Mathematical analysis
Mathematical models
Rational spectral collocation method
Spectra
Third-order singularly perturbed problems
Transformations
Third-order singularly perturbed problems
Asymptotic expansion
Rational spectral collocation method
Boundary layer
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ISSN0377-0427
1879-1778
DOI10.1016/j.cam.2016.03.009

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Summary: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.
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ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2016.03.009