Open Access

Jörg Ackermann, Michael Wulkow

• The description of chain length distributions in macromolecular reaction kinetics leads to so-called countable systems of differential equations. In particular, when the appearing reaction rate coefficients depend on the chain length of the reacting macromolecules itself, an efficient numerical treatment of these systems is very difficult. Then even the evaluation of the right-hand side of the system can become prohibitively expensive with respect to computing time. In this paper we show how the discrete Galerkin method can be applied to such problems. The existing algorithm CODEX is improved by use of a multiplicative error correction scheme for time discretization and a new type of numerical preprocessing by means of a Gauss summation. Both ideas are exemplary for a wide class of approximation types and are described very briefly here. The new numerical techniques are tested on an example from soot formation, where the coagulation of molecules is modeled in terms of reaction coefficients depending on the surface of the particles and their collision frequency.