The use of cubic splines in the numerical solution of a system of second-order boundary value problems

We use uniform cubic polynomial splines to develop some consistency relations which are then used to develop a numerical method for computing smooth approximations to the solution and its derivatives for a system of second-order boundary value problems associated with obstacle, unilateral, and contact problems. We show that the present method gives approximations which are better than those produced by other collocation, finite difference, and spline methods.