Abstract
Abstract In this paper, we consider the construction of the sextic splines function which interpolating the lacunary data. Also, under suitable conditions, we show that the existence and uniqueness of the solution. The convergence analysis of this spline function is studied and the error bounds are derived. This spline function applied to find an approximate value of a given function and its derivatives through six orders. A numerical example has been given to show the applicability and efficiency of the new proposed technique.
