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On the use of series to integrate rate equations
Author(s) -
Poland Douglas
Publication year - 1990
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.540110313
Subject(s) - series (stratigraphy) , radius of convergence , power series , recursion (computer science) , monotonic function , mathematics , nonlinear system , variable (mathematics) , function (biology) , convergence (economics) , rate of convergence , mathematical analysis , computer science , algorithm , physics , paleontology , channel (broadcasting) , computer network , quantum mechanics , evolutionary biology , economics , biology , economic growth
The coefficients in power series, in the variable time, describing coupled nonlinear chemical reactions are easily obtained from a recursion relation. Since these series have a limited radius of convergence they are not very useful as such. If the series are inverted to give time as a function of the appropriate power of a progress variable, the new series converge over the entire time course of the reaction. If, further, the long‐time asymptotic behavior, obtained from the linearized kinetic equations, is used, one can obtain a series expansion for a function that describes the correct short‐time behavior. This function can be estimated very well using truncated series. The method works well for consecutive nonlinear reactions where the progress variables are monotonic functions of time; this includes many cases where the concentrations of intermediate species go through a maximum as the reaction progresses.