Certain implementative applications of Separate Node Ascending Derivatives Expansion (SNADE)

Abstract

In this work we have focused on a very recently developed method called as Separate Node Ascending Derivatives Expansion (SNADE). SNADE can be considered as an infinite interpolation like Taylor Series Expansion. A Taylor Series is an infinite sum representation whose terms are calculated from the values of the functions derivatives at a single point. This newly proposed method involves denumerable infinitely many nodes in contrast to Taylor Series Expansion. SNADE is based on derivative integration formula for a univariate function. Integral of derivative identity is not only required to be used for the target function but repetitiously for its all derivatives. It may not be required to be used in the same interval. In addition to all these, each derivative value becomes evaluated at a different independent variable value. This work is designed to emphasize on the methods interpolatory nature. For this purpose certain implementation results are given and compared with well-known interpolation methods.