Non-polynomial sextic spline approach for the solution of fourth-order boundary value problems

In this paper a non-polynomial sextic spline function is applied to the numerical solution of a linear fourth-order two-point boundary-value problem occurring in a plate deflection theory. We have developed a non-polynomial sextic spline, which reduces to ordinary sextic spline as θ → 0. Spline relations and error estimates are given. Direct methods of order two, four and six have been obtained. Numerical results are provided to demonstrate the superiority of our methods.