This paper is concerned with the numerical approximation by compact finitedifference schemes of differential operators of the form Leu = eu(m) + ^Jv=0 avv^ without turning points. The stability of L£ combined with various auxiliary conditions is discussed, and a representation result for solutions of problems involving it is proven. This representation decomposes the solution into a smooth oute...

This work develops an ε-uniform finite element method for singularly perturbed two-point boundary value problems. A surprising and remarkable observation is illustrated: By inserting one node arbitrarily in any element, the new finite element solution always intersects with the original one at fixed points, and the errors at those points converge at the same rate as regular boundary value probl...

A new kind of numerical method based on rational spectral collocation with the sinh transformation is presented for solving parameterized singularly perturbed two-point boundary value problems with one boundary layer. By means of the sinh transformation, the original Chebyshev points are mapped onto the transformed ones clustered near the singular points of the problem. The results from asympto...