Numerical method for a system of fourth-order boundary value problems

In this paper we use sextic polynomial splines to derive some consistency relations which are then used to develop a numerical method for computing the solution for a system of fourth order boundary-value problems associated with obstacle, unilateral and contact problems. We show that a class of variational inequalities related to contact problems in elasto-statics can be characterized by a sequence of variational equations, which are solved using numerical method. For the purpose of numerical illustrations, we consider example of an elastic beam lying over an elastic obstacle. We have developed the boundary formulas of order four to restrict the band width of the coefficient matrix of the linear system to five. The numerical illustrations and comparison with other methods are given which shows the advantage of the present scheme.