A fourth/second order accurate collocation method for singularly perturbedtwo-point boundary value problems using tension splines

The collocation tension spline is considered as a numerical solution of a s ingularly perturbed two-point boundary value problem: epsilony " + by' + cy = f. The collocation points are chosen as a generalization of the classica l Gaussian points. Unlike the traditional approach, we employ the B-spline representation in the analysis. This leads to global quadratic convergence of the method for small perturbation parameters, and, for large values, the order of convergence is four.