Theoretical Chemistry Accounts

, 124:303 | Cite as

Numerical solution methods for large, difficult kinetic master equations

  • Terry J. Frankcombe
  • Sean C. SmithEmail author
Feature Article


The kinetics of gas-phase reactions, including pressure-dependent weak collision and non-equilibrium effects, can be modelled using a master equation. In this paper, we address the practical computational problem of finding solutions to such kinetic master equations. The mathematical structure of the master equation can be utilised to develop a number of specialised numerical techniques that are capable of solving the master equation in the presence of difficult numerics and for large problems. The former is important for modelling low temperature and pressure systems, and the latter is important for modelling the large networks of isomerising species common in combustion chemistry applications. We focus on numerical methods that exhibit particular practical use because of their robust nature or scalability to many isomers, or both. Recent developments in linear-scaling methods are highlighted.


Master equation Multi-well Energy grained Numerical integration Collisional energy transfer 


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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Research School of ChemistryAustralian National UniversityCanberraAustralia
  2. 2.Australian Institute of Bioengineering and NanotechnologyUniversity of QueenslandSt. LuciaAustralia

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