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.