Geodesic
Decomposition of the problem in the numerical solution of differential-algebraic systems for chemical reactions with partial equilibria
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 15 (2022) no. 4, pp. 59-70

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The paper considers two simple systems of differential-algebraic equations that appear in the study of chemical kinetics problems with partial equilibria: some of the variables are determined from the condition argmin for some system function state, which depends on all variables of the problem. For such a statement, we can write a differential-algebraic system of equations where the algebraic subproblem expresses the conditions for the minimality of the state function at each moment. It is convenient to use splitting methods in numerical solving, i.e. to solve dynamic and optimization subproblems separately. In this work, we investigate the applicability of differential-algebraic splitting using two simplified systems. The convergence and order of accuracy of the numerical method are determined. Different decomposition options are considered. Calculations show that the numerical solution of the split system of equations has the same order of accuracy as the numerical solution of the joint problem. The constraints are fulfilled with sufficient accuracy if the procedure of the numerical method ends with the solution of the optimization subproblem. The results obtained can be used in the numerical solving of more complex chemical kinetics problems.
Keywords: differential-algebraic systems, optimization, numerical methods. 
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     author = {I. G. Donskoy},
     title = {Decomposition of the problem in the numerical solution of differential-algebraic systems for chemical reactions with partial equilibria},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
     pages = {59--70},
     publisher = {mathdoc},
     volume = {15},
     number = {4},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VYURU_2022_15_4_a4/}
}
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I. G. Donskoy. Decomposition of the problem in the numerical solution of differential-algebraic systems for chemical reactions with partial equilibria. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 15 (2022) no. 4, pp. 59-70. http://geodesic.mathdoc.fr/item/VYURU_2022_15_4_a4/