non-polynomial quartic spline solution of boundary-value problem

quartic non-polynomial spline function approximation in off step points is developed, for the solution of fourth-order boundary value problems. using consistency relation of such spline and suitable choice of parameter,we have obtained second, fourth and sixth orders methods. convergence analysis of sixth order method has been given. the methods are illustrated by some examples, to verify the order of accuracy of the presented methods. the computed results are compared with other exiting methods, collocation, decomposition and spline methods. computed result verify the applicability and accuracy of our presented methods.