Frankcombe, Terry J.Smith, Sean C.2015-11-102015-11-100021-9606http://hdl.handle.net/1885/16457In this paper we propose a second linearly scalable method for solving large master equations arising in the context of gas-phase reactive systems. The new method is based on the well-known shift-invert Lanczos iteration using the GMRES iteration preconditioned using the diffusion approximation to the master equation to provide the inverse of the master equation matrix. In this way we avoid the cubic scaling of traditional master equationsolution methods while maintaining the speed of a partial spectral decomposition. The method is tested using a master equation modeling the formation of propargyl from the reaction of singlet methylene with acetylene, proceeding through long-lived isomerizing intermediates.We gratefully acknowledge the support of the Australian Research Council in funding this work ~Discovery Project Grant No. DP0211019http://www.sherpa.ac.uk/romeo/issn/0021-9606..."Publishers version/PDF may be used on author's personal website, institutional website or institutional repository" from SHERPA/RoMEO site (as at 11/11/15). Copyright 2003 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in The Journal of Chemical Physics and may be found at https://doi.org/10.1063/1.1628214Keywords: Acetylene; Algorithms; Approximation theory; Eigenvalues and eigenfunctions; Integration; Isomerization; Matrix algebra; Ordinary differential equations; Pressure; Rate constants; Temperature; Vectors; Cholesky factorization; Diffusion approximation; Gas2003-12-2210.1063/1.16282142015-12-09