Abstract. We introduce piecewise interpolating polynomials as an approximation for the driving terms in the numerical solution of the singularly perturbed differential equation. In this way we obtain the difference scheme which is second order accurate in uniform norm. We verify the convergence rate of presented scheme by numerical experiments.
2000 Mathematics Subject Classification. 65L10.
Key words and phrases. Singularly perturbed self-adjoint problem, interpolating splines, collocation method, uniform convergence in a small parameter.