On the numerical solution of the general kinetic “K-angle” reaction system

Abstract

In a recent paper by Tobias and Tasi in this journal the authors discuss the “K-angle” kinetic problem and focus on its analytic solution for \(K\le 5\). The authors correctly mention that the case \(K>5\) requires numerical treatment in the part of the procedure where the eigenvalues of the characteristic polynomial are determined by solving an algebraic equation of degree greater than or equal to five. In this work we focus on this algorithmic part by suggesting a suitable and effective numerical procedure. For the sake of simplifying the numerical procedure and to formulate the whole algorithm in an easy programmable way we reformulate the “K-angle” problem by introducing double indices for the reactions between the components. This notation allows to greatly simplify the formulation of the problem and the description of the whole algorithmic procedure and facilitates the creation of appropriate programming tools. We present an example of such a tool, namely a software module named K-angle within the programming environment of CAS Mathematica possessing certain visualization properties.