An analytical method for modeling first-order decay networks

A wide range of numerical methods are available to integrate coupled differential equations for first-order decay networks. When greatly differing decay rates exist in a reaction network, the stiffness of ordinary differential equations increases and requires additional effort to obtain solutions numerically. Although analytical solutions are preferred, they are limited to relatively simple reaction networks and small numbers of species. In this paper, we propose a methodology for formulating analytical solutions of ODEs for an unlimited number of species and more generalized reaction networks, including multidaughter branching and multiparent converging reactions. The derivation of analytical solutions for user-defined first-order reaction networks is implicitly implemented as a generalized computer code. Then, derived analytical solutions of the first-order reactions are coupled with numerical solutions for transport using an operator-splitting scheme. The solution method is then used to obtain analytical solutions of transport systems coupled by complex decay networks.

► We developed a decomposition method for modeling first-order decay networks analytically.
► The decomposition method is applicable to all first-order decay networks, including sequential, multidaughter branching, and multiparent converging reactions.
► We coupled analytical solutions of first-order reactions with numerical solutions of advection and dispersion in a hybrid operator-splitting (OS) scheme.
► The hybrid OS scheme is computationally efficient, accurate, and robust.