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

Quartic non-polynomial splines are used to develop a new numerical method for computing approximations to the solution of a system of third-order boundary-value problems associated with obstacle, unilateral, and contact problems. It is shown that the new method gives approximations, which are better than those produced by other collocation, finite-difference, and spline methods. Convergence analysis of the method is discussed through standard procedures. A numerical example is given to illustrate the applicability and efficiency of the novel method.