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Computational aspects of master equation transformation in terms of moments
Author(s) -
Gidiotis Grigorios,
Forst Wendell
Publication year - 1987
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.540080419
Subject(s) - master equation , vandermonde matrix , mathematics , coefficient matrix , matrix (chemical analysis) , observable , normalization (sociology) , differential equation , population balance equation , population , mathematical analysis , physics , quantum mechanics , chemistry , sociology , quantum , eigenvalues and eigenvectors , demography , chromatography , anthropology
The master equation describing the temporal evolution of a gaseous system in contact with a heat bath can be transformed into a system of linear, constant‐coefficient, first‐order differential equations of moments of the population distribution. While it has the advantage that populations are obtained directly from observables (moments), this system of equations is not too well‐conditioned and unless precautions are taken, unsurmountable numerical problems appear. These are principally associated with manipulations (inversion and taking the exponential of a matrix) involving slightly modified Vandermonde matrices whose elements span a very wide range of orders of magnitude. This article discusses ways to avoid these pitfalls which consist principally of a suitable matrix normalization.