A survey on parametric spline function approximation

This survey paper contains a large amount of material and indeed can serve as an introduction to some of the ideas and methods for the solution of ordinary and partial differential equations starting from Schoenberg's work [Quart. Appl. Math. 4 (1946) 345-369]. The parametric spline function which depends on a parameter ω > 0, is reduces to the ordinary cubic or quintic spline for ω = 0. A note on parametric spline function approximation, which is special case of this work has been published in [Comp. Math. Applics. 29 (1995) 67-73]. This article deals with the odd-order parametric spline relations.