Effect of Random Variation of the Initial Values of Ordinary Differential Equations and its Web-based Application to Chemical Kinetics

In this article, the initial values of ordinary differential equations (ODEs) are computationally subjected to random variation in order to assess its effect on the final values, through a Monte Carlo procedure, with a chemical kinetics problem as the mathematical illustration. As we use and uphold the Web as a computing medium, the results can be verified on constructed, public web pages. A random variation in the reactants’ composition raises undesired variation, which we observe, in the product composition. In a preliminary part of the article: we overview the determination of ODEs’ parameters from data, leading, with Python, to favor its 'minimize' function, against 'curve fit'; and we use some reactions to find their rate constants, namely, the frequent A  B  C (or “ABC”) reaction, as the one to produce furfural. In the main part of the article, we assess the variation in the final values, the product composition, in the ABC reaction using Monte Carlo simulation, by repeatedly solving its ODEs, through numerical integration to keep generality, the initial values being assumed Gaussian. The final values are simulated on the web pages for exploration, showing the Web as a medium for scientific computing and use in publications, also easing the academia-industry connection.