In this paper the quadratic spline difference scheme for a convection-diffusion problem is derived. With the suitable choice of collocation points we provide the discrete minimum principle. The numerical results implies the uniform convergence of order O(n −2 ln 2 n).
The linear singularly perturbed reaction-diffusion problem is considered. The spline difference scheme on the Shishkin mesh is used to solve the problem numerically. With the special position of collocation points, the obtained scheme satisfies the discrete minimum principle. Numerical experiments which confirm theoretical results are presented.