Separate multinode ascending derivatives expansion (Demiralp’s SMADE): Basis polynomials

Abstract

Separate Multinode Ascending Derivatives Expansion (SMADE) is a recently developed function representation method based on “Separate Node Ascending Derivatives Expansion (SNADE)” which was proposed by Prof. Demiralp. For this reason we call this method in this work “Demiralp’s SMADE”. The basic difference between two methods is that SNADE uses one separate node for each derivative to construct the expansion while SMADE uses multinodes for the same entities even though the separate nature of the nodes is not mandatory. This study focuses on SMADE both to present all important details of the method including its formulation and its basis polynomials.