Rational Spectral Collocation Method for a Coupled System of Singularly Perturbed Boundary Value Problems
Suqin Chen 1, Yingwei Wang 1, Xionghua Wu 11 Department of Mathematics, Tongji University, Shanghai 200092, China
Received 2010-6-11 Accepted 2010-12-28
Available online 2011-6-27
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.
Key words: Singular perturbation, Coupled system, Rational spectral collocation method, Boundary layer, Reaction-diffusion, Convection-diffusion.
AMS subject classifications: 65L10, 65M70.
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