Numerical Methods for Ordinary Differential Equations Systems with Small Parameter with Applications in Kinetics Chemistry

Ilea Mihai

Numerical Methods for Ordinary Differential Equations Systems with Small Parameter with Applications in Kinetics Chemistry

  • Author Ilea Mihai
  • Co-Author Turnea Marius, Rotariu Mariana, Arotaritei Dragos, Gheorghita Andrei
  • DOI
Keywords : Chemical kinetics Reaction, Numerical Methods, Matlab, Small Parameter


Abstract

Mathematical modelling is a more and more frequently used working tool, located, in this particular case, at the intersection between two basic sciences: mathematics and chemistry. We can wonder: can mathematical models offer predictions on the evolution of a chemical reaction? .Chemical reactions of a wide variety can be modelled with coupled differential equations. These describe the time evolution of the concentrations of the various chemical species: reactants, intermediaries, catalysts, and products. Such problems are quite simple to set up and solve with Matlab. The Matlab functions can numerically integrate the differential equations that arise. The resulting concentrations can be plotted as a function of time and also be used to accurately compute the expected concentration of the molecular species. The use of MATLAB in this article illustrates the important role of informatics in research in chemical reactions modelling. An important advantage of using a numerical method is that the mathematical representation of the chemical processes allows transparency and correctness in relation to chemical assumptions, thus allowing us to test our understanding on the chemical reactions by comparing the graphs obtained with other chemical models observed.

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