Uniform convergence difference schemes for singularly perturbed mixed boundary problems

In this paper, we consider the conservative form of singularly perturbed ordinary differential equations with mixed boundary conditions. A fitted mesh finite difference scheme is constructed for these problems. The scheme is shown to be uniformly convergent with respect to the perturbed parameter. A class of conservative difference schemes with uniform mesh are also considered. These difference schemes are proved to be first-order uniformly convergent. The computed results for both cases are in good agreement with the exact solutions.