A class of methods based on non-polynomial spline functions for the solution of a special fourth-order boundary-value problems with engineering applications

We use a quintic non-polynomial spline functions to develop a numerical method for computing approximations to the solution of a system of fourth-order boundary-value problems associated with plate deflection theory. We show that the present family of methods gives better approximations and generalize all the existing finite difference and spline functions based methods up to order six. Convergence of the methods is shown through standard convergence analysis. Numerical exampls are given to illustrate the applicability and efficiency of the new method.