Explicit ODE solution sensitivities to initial impositions: PREVTH evaluations for Henon-Heiles system

Abstract

This paper is based on the CMMSE 2017 Proceedings paper having a  different title given by the authors Melike Ebru K\i rk\i n and  Metin Demiralp. Almost all parts of this paper except two sections  about Conical PREVTH and sensitivity coefficient recursions have  been newly created after conference even though these two exceptional sections' material have been mostly taken from that resource  since they have become somehow standard. New parts involve conceptuality and applications and completely new confirmative implementations based on certain functional relations amongst the components of Henon-Heiles system unknowns vector. Hence, we have not checked only the self-consistencies but focused on comparisons between the  certain functional values and zero constant function. The conicality matrix determination, based on Constancy Adding Space Extension (CASE), has been presented in a sufficiently detailed manner. Beyond that the confirmation of the result's validity has also been given explicitly. These are basic post-CMMSE-17 originalities.