A Spectral Collocation Method for Systems of Singularly Perturbed Boundary Value Problems

We present a spectrally accurate method for solving coupled singularly perturbed second order two-point boundary value problems (BVPs). The method combines analytical coordinate transformations with a standard Chebyshev spectral collocation method; it is applicable to linear and to nonlinear problems. The method performs well in resolving very thin boundary layers. Compared to other methods which had been proposed for systems of BVPs this method is competitive in terms of accuracy, allows for different perturbation parameters in each of the equations, and does not require special properties of the coefficient functions.