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Volume 29, Issue 4
Rational Spectral Collocation Method for a Coupled System of Singularly Perturbed Boundary Value Problems

Suqin Chen, Yingwei Wang, & Xionghua Wu

J. Comp. Math., 29 (2011), pp. 458-473.

Published online: 2011-08

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  • Abstract

A novel collocation method for a coupled system of singularly perturbed linear equations is presented. This method is based on rational spectral collocation method in barycentric form with sinh transform. By sinh transform, the original Chebyshev points are mapped into the transformed ones clustered near the singular points of the solution. The results from asymptotic analysis about the singularity solution are employed to determine the parameters in this sinh transform. Numerical experiments are carried out to demonstrate the high accuracy and efficiency of our method.

  • AMS Subject Headings

65L10, 65M70.

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COPYRIGHT: © Global Science Press

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@Article{JCM-29-458, author = {}, title = {Rational Spectral Collocation Method for a Coupled System of Singularly Perturbed Boundary Value Problems}, journal = {Journal of Computational Mathematics}, year = {2011}, volume = {29}, number = {4}, pages = {458--473}, abstract = {

A novel collocation method for a coupled system of singularly perturbed linear equations is presented. This method is based on rational spectral collocation method in barycentric form with sinh transform. By sinh transform, the original Chebyshev points are mapped into the transformed ones clustered near the singular points of the solution. The results from asymptotic analysis about the singularity solution are employed to determine the parameters in this sinh transform. Numerical experiments are carried out to demonstrate the high accuracy and efficiency of our method.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1103-m3434}, url = {http://global-sci.org/intro/article_detail/jcm/8487.html} }
TY - JOUR T1 - Rational Spectral Collocation Method for a Coupled System of Singularly Perturbed Boundary Value Problems JO - Journal of Computational Mathematics VL - 4 SP - 458 EP - 473 PY - 2011 DA - 2011/08 SN - 29 DO - http://doi.org/10.4208/jcm.1103-m3434 UR - https://global-sci.org/intro/article_detail/jcm/8487.html KW - Singular perturbation, Coupled system, Rational spectral collocation method, Boundary layer, Reaction-diffusion, Convection-diffusion. AB -

A novel collocation method for a coupled system of singularly perturbed linear equations is presented. This method is based on rational spectral collocation method in barycentric form with sinh transform. By sinh transform, the original Chebyshev points are mapped into the transformed ones clustered near the singular points of the solution. The results from asymptotic analysis about the singularity solution are employed to determine the parameters in this sinh transform. Numerical experiments are carried out to demonstrate the high accuracy and efficiency of our method.

Suqin Chen, Yingwei Wang, & Xionghua Wu. (1970). Rational Spectral Collocation Method for a Coupled System of Singularly Perturbed Boundary Value Problems. Journal of Computational Mathematics. 29 (4). 458-473. doi:10.4208/jcm.1103-m3434
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