Separate node ascending derivatives expansion (SNADE) for univariate functions: Conceptuality and formulation

Abstract

This work somehow focuses on the construction of a new Taylor expansion involving denumerable infinitely many nodes. It is a combined utilization of derivative integration formula for a univariate function with the expansions at different nodal points. This paper presents the conceptual sides of the expansion and gives the explicit formulation which involves multiparameter polynomials and again a multiparameter remainder term. Certain implicit and explicit recursions amongst the polynomials, a bound for the remainder term and the convergence of the scheme are presented in the second companion SNADE paper of this proceedings while the third companion SNADE paper focuses on the univariate integration. Node optimization via partial fluctuation suppression is given in the fourth SNADE paper.