Convergence of numerical solution of a fourth-order boundary value problem

Quintic spline procedure for the solution of a fourth-order boundary value problem is developed, spline relations are derived, boundary condition formula of orders O(h6) and O(h8) are formulated. The convergence of prescribed method is proved, the matrix associated with the system of linear equations that arises is not required to be monotone, the only requirement is that f(x) be positive. Numerical illustration are given.