STABILITY OF O.D.E. SOLUTIONS CORRESPONDING TO CHEMICAL MECHANISMS BASED-ON UNIMOLECULAR FIRST ORDER REACTIONS

Authors : Victor MARTINEZLUACES

Pages : 58-63

Doi:10.36753/mathenot.421332

View : 35 | Download : 9

Publication Date : 2015-10-30

Article Type : Research Paper

Abstract :The most simple unimolecular first order chemical reaction mechanism that involves two species, can be exemplified by the Mutarotation of Glucose [1]. The corresponding mathematical model is an O.D.E. linear system which solutions are stable, but not asymptotically [2]. When three chemical compounds are considered, the mechanism can vary from a simple two reactions sequence to a complicated one as the adsorption of Carbon Dioxide insert ignore into journalissuearticles values(CO2); over Platinum insert ignore into journalissuearticles values(P t); surfaces [2]. Although in these examples the mechanisms are very different, in both cases the O.D.E. system has two negative eigenvalues and the other one is zero. Once again, solutions show a weak stability which implies that small errors due to measurements in the initial concentrations will remain bounded, but they do not tend to vanish as the reaction proceeds. In this paper, a general result for reversible reactions is stated through an inverse modelling approach [3] [4], proposing theoretical mechanisms and showing algebraically that all the eigenvalues are negative, except one, which is zero. From this fact, the conclusions about the stability of the solutions are obtained and their consequences on the propagation of measurements errors are analysed.
Keywords : Chemical mechanisms, O D E linear systems, Solutions stability

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