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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

DOI: 10.4208/jcm.1103-m3434

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.

  • Keywords

Singular perturbation, Coupled system, Rational spectral collocation method, Boundary layer, Reaction-diffusion, Convection-diffusion.

  • AMS Subject Headings

65L10, 65M70.

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{JCM-29-458, author = {Suqin Chen, Yingwei Wang, and Xionghua Wu}, 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 AU - Suqin Chen, Yingwei Wang, & Xionghua Wu 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, and Xionghua Wu. (2011). 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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