Non polynomial spline approach to the solution of a system of third-order boundary-value problems

We use a quartic spline equivalent nonpolynomial spline functions to develop a numerical method for computing approximations to the solution of a system of third-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. A numerical example is given to illustrate the applicability and efficiency of the new method.