Analysis by modified power series of differential equations applied to chemical kinetics
DOI:
https://doi.org/10.47187/perf.v1i35.375Keywords:
nonlinear differential equations, kinetic chemistry, modified power seriesAbstract
Using nonlinear differential equations, the kinetics of successive homogeneous elementary chemical reactions occurring simultaneously can be described. Subsequently, the mathematical model that is deduced from the law of mass action is presented and is solved using modified power series to define the functions that govern the phenomenon. This article interprets the oscillations resulting from differential equations, denoting the interaction of the reactions affected by their previous states. The oscillations before the stabilization of the reaction can be interpreted as the reaction rate. When doing so by power series, it can be denoted that the current behavior is affected by the previous behavior, affected by the monotony of the function, and the analysis of its changes in previous instants. This work shows an introduction to Differential Equations with delay applied to the observation of chemical reactions, mainly the aspect of delay in a chemical reaction that must be considered in all cases of reactions, to know the consequences that are carried out after taking into consideration previous times and their respective optimization cases.
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Castro MA, Mayorga CJ, Sirvent A, Rodríguez F. Exact numerical solutions and high order nonstandard difference schemes for a second order delay differential equation. Math Methods Appl Sci. 2023;46(23):17962–17979. doi:10.1002/mma.9540.
Castro MA, Sirvent A, Rodríguez F. Nonstandard finite difference schemes for general linear delay differential systems. Math Methods Appl Sci. 2021;44(6):3985–3999.
Edwards CH, Penney DE. Ecuaciones diferenciales elementales con aplicaciones. México: Prentice-Hall Hispanoamericana; 1986.
García MA, Castro MA, Martín JA, Rodríguez F. Exact and nonstandard numerical schemes for linear delay differential models. Appl Math Comput. 2018;338:337–345.
García MA, Castro MA, Martín JA, Rodríguez F. Exact and nonstandard finite difference schemes for coupled linear delay differential systems. Mathematics. 2019;7(11):1038. doi:10.3390/math7111038.
Atkins P, Overton T, Rourke J, Weller M, Armstrong F. Shriver and Atkins’ Inorganic Chemistry. 5th ed. New York: Oxford University Press; 2010.
Atarés Huerta LM. Fundamentos de cinética química: ecuación cinética [Internet]. 2011 [cited 2026 Feb 11]. Available from: https://riunet.upv.es/handle/10251/12661
Avery H. Basic Chemical Kinetics and Reaction Mechanisms. Barcelona: Editorial Reverté; 1977.
Çengel YA, Palm WJ. Differential Equations for Engineering and Science. New York: McGraw-Hill; 2014.
Epstein IR, Pojman JA. An Introduction to Nonlinear Chemical Dynamics. New York: Oxford University Press; 1998.
Felder RM, Rousseau RW. Principios elementales de los procesos químicos. 2nd ed. Wilmington: Addison-Wesley Iberoamericana; 1991.
Himmelblau DM. Principios básicos y cálculos en ingeniería química. 6th ed. México: Prentice-Hall Hispanoamericana; 1997.
Housecroft CE, Sharpe AG. Química inorgánica. 2nd ed. Madrid: Pearson Educación; 2006.
House J, House K. Descriptive Inorganic Chemistry. 3rd ed. London: Elsevier; 2016.
Williams DLH. Synthesis, properties, and reactions of S-nitrosothiols. In: Williams DLH, editor. Nitrosation Reactions and the Chemistry of Nitric Oxide. Amsterdam: Elsevier; 2004. p. 137–160.
Mayorga Arias CJ. Soluciones numéricas exactas y esquemas en diferencias finitas no estándar para ecuaciones diferenciales con retardo [tesis doctoral]. Alicante (Spain): Universidad de Alicante; 2024.
Mayorga CJ, Castro MA, Sirvent A, Rodríguez F. On the construction of exact numerical schemes for linear delay models. Mathematics. 2023;11(8):1836. doi:10.3390/math11081836.
Hale JK, Verduyn Lunel SM. Introduction to Functional Differential Equations. New York: Springer; 1993.
Diekmann O, van Gils SA, Verduyn Lunel SM, Walther HO. Delay Equations: Functional-, Complex-, and Nonlinear Analysis. New York: Springer; 1995.
Mickens RE. Nonstandard Finite Difference Schemes: Methodology and Applications. Singapore: World Scientific; 2021.
Levenspiel O. Engineering of Chemical Reactions. Barcelona: Editorial Reverté; 1981.
Rayner-Canham G, Overton T. Descriptive Inorganic Chemistry. 5th ed. New York: W. H. Freeman; 2010.
Smith JM. Ingeniería de la cinética química. 3rd ed. México: Compañía Editorial Continental; 1995.
Wang PG, Cai T, Taniguchi N. Nitric Oxide Donors for Pharmaceutical and Biological Applications. New York: John Wiley & Sons; 2005.
Wang PG, Xian M, Tang X, Wu X, Wen Z, Cai T, et al. Nitric oxide donors: chemical activities and biological applications. Chem Rev. 2002;102(4):1091–1134.
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