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DECOMPOSITION OF THE PROBLEM IN THE NUMERICAL SOLUTION OF DIFFERENTIAL-ALGEBRAIC SYSTEMS FOR CHEMICAL REACTIONS WITH PARTIAL EQUILIBRIA [ДЕКОМПОЗИЦИЯ ЗАДАЧИ ПРИ ЧИСЛЕННОМ РЕШЕНИИ ДИФФЕРЕНЦИАЛЬНО-АЛГЕБРАИЧЕСКИХ СИСТЕМ ДЛЯ ХИМИЧЕСКИХ РЕАКЦИЙ С ЧАСТИЧНЫМИ РА

Статья в журнале
Donskoy I.G.
Bulletin of the South Ural State University, Series: Mathematical Modelling, Programming and Computer Software
2022
DECOMPOSITION OF THE PROBLEM IN THE NUMERICAL SOLUTION OF DIFFERENTIAL-ALGEBRAIC SYSTEMS FOR CHEMICAL REACTIONS WITH PARTIAL EQUILIBRIA [ДЕКОМПОЗИЦИЯ ЗАДАЧИ ПРИ ЧИСЛЕННОМ РЕШЕНИИ ДИФФЕРЕНЦИАЛЬНО-АЛГЕБРАИЧЕСКИХ СИСТЕМ ДЛЯ ХИМИЧЕСКИХ РЕАКЦИЙ С ЧАСТИЧНЫМИ РА
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. © 2022 South Ural State University. All rights reserved.

Библиографическая ссылка

Donskoy I.G. DECOMPOSITION OF THE PROBLEM IN THE NUMERICAL SOLUTION OF DIFFERENTIAL-ALGEBRAIC SYSTEMS FOR CHEMICAL REACTIONS WITH PARTIAL EQUILIBRIA [ДЕКОМПОЗИЦИЯ ЗАДАЧИ ПРИ ЧИСЛЕННОМ РЕШЕНИИ ДИФФЕРЕНЦИАЛЬНО-АЛГЕБРАИЧЕСКИХ СИСТЕМ ДЛЯ ХИМИЧЕСКИХ РЕАКЦИЙ С ЧАСТИЧНЫМИ РАВНОВЕСИЯМИ] // Bulletin of the South Ural State University, Series: Mathematical Modelling, Programming and Computer Software. Vol.15. №4. 2022. P.59-70. DOI: 10.14529/mmp220405
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