Rational Spectral Collocation Method for a Coupled System of Singularly Perturbed Boundary Value Problems

Rational Spectral Collocation Method for a Coupled System of Singularly Perturbed Boundary Value Problems

Year:    2011

Journal of Computational Mathematics, Vol. 29 (2011), Iss. 4 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1103-m3434

Journal of Computational Mathematics, Vol. 29 (2011), Iss. 4 : pp. 458–473

Published online:    2011-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    16

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

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