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In this paper, we use parametric quintic splines to derive some consistency relations which are then used to develop a numerical method for computing the solution of a system of fourth-order boundary-value problems associated with obstacle, unilateral, and contact problems. It is known that a class of variational inequalities related to contact problems in elastostatics can be characterized by a sequence of variational inequations, which are solved using some numerical method. Numerical evidence is presented to show the applicability and superiority of the new method over other collocation, finite difference, and spline methods. [ABSTRACT FROM AUTHOR]

We use parametric cubic spline functions to develop a numerical method for computing approximations to the solution of 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. A numerical example is given to illustrate the applicability and efficiency of the new method. [ABSTRACT FROM AUTHOR]

A fourth-order uniform mesh difference scheme using quintic splines for solving a singularly-perturbed boundary-value problem of the form is derived. Our scheme leads to a pentadiagonal linear system. The convergence analysis is given and the method is shown to have fourth-order convergence. Numerical illustrations are given to confirm the theoretical analysis of our method. [ABSTRACT FROM AUTHOR]